![Foundation of
Aversa, 1030.
The sons of
Tancred of
Hauteville.
Conquest of Apulia,
1041–2.
1022 [see page 50], he found his chief obstacle in the new Greek
fortress of Troja, obstinately defended by some valiant Normans in
the pay of their old foe the Catapan.
Other Normans now flocked to the land of promise. Among these
was a chieftain named Ranulf, who joined Sergius, Prince of Naples,
a vassal of the Greeks, in his war against the Lombard prince Pandulf
of Capua. In reward for his services Ranulf received one of the
richest districts of the Terra di Lavoro, where he built in 1030 a town
named Aversa, the first Norman settlement in Italy. This foundation
makes a new departure in Norman policy.
The Normans no longer came to Italy as
isolated adventurers willing to sell their swords to the highest bidder.
By much the same arts as those by which their brethren later got
hold of the fairest parts of Wales and Ireland, the adventurers strove
to carve feudal states for themselves out of the chaos of southern
Italy. Whilst cleverly utilising the feuds that raged around them, they
pursued their interests with such dexterity, courage, and clear-
headed selfishness, that brilliant success soon crowned their efforts.
Conrad II. sojourned at Capua in 1038, deposed Pandulf and
confirmed Ranulf in the possession of Aversa, which he erected into
a county owing homage to the Western Emperor. Three of the twelve
sons of the Norman lord, Tancred of Hauteville, now left their scanty
patrimony in the Côtentin and joined the Normans in Italy. Their
names were William of the Iron Arm, Drogo, and Humphrey. In
1038 they joined the Greeks under George
Maniaces in an attempt to expel the
Mohammedans from Sicily. Messina and
Syracuse were captured, but an affront to their companion-in-arms
Ardouin drove the Normans back to the mainland in the moment of
victory, and led them to wreak their vengeance on the Greeks by a
strange compound of violence and treachery. Ardouin their friend
took the Greek pay and became governor of Melfi, the key of Apulia.
He proposed to the Normans that he should deliver Melfi to them,
and make that a starting-point for the conquest of Apulia, which he
proposed to divide between them and himself. The northerners
accepted his proposals. In 1041 Melfi was
delivered into their hands, and a long war
broke out between them and their former allies. By shrewdly putting
Adenulfus, the Lombard Duke of Benevento at the head of their](https://image.slidesharecdn.com/46259-250404071409-95dd221f/85/Time-Series-Analysis-Fourth-Edition-George-E-P-Box-27-320.jpg)
![Hildebrand’s early
career and
character.
We have now come to one of the real
crises of history. The new spirit had gained
ascendency at Rome, and the great man had
arisen who was to present the papal ideal with all the authority of
genius. Hildebrand of Soana[6]
was the son of a well-to-do Tuscan
peasant; he had been brought up by his uncle, abbot of the strict
convent of St. Mary’s on the Aventine, which was the centre of the
Cluniac ideas in Rome, and where he made his profession as monk.
He became the chaplain of Gregory VI. who, though he bought the
Papacy with gold, had striven his best to carry out the work of
reformation. When deprived of his office at Sutri, Gregory VI. had
been compelled to retire to Germany with the Emperor. Hildebrand,
now about twenty-five years old, accompanied his master in his exile.
In 1048 the deposed Pope died, and his chaplain betook himself to
Cluny, where he remained for a full year, and where, he tells us, he
would have gladly spent the rest of his life. But in 1049 Leo IX. passed
through Cluny on his way to Rome, and Hildebrand was commanded
to accompany him. With his return to Rome his active career began.
As papal sub-deacon he reorganised the crippled finances of the Holy
See, and strengthened the hold of the Pope over the unruly citizens.
As papal legate he was sent to France in 1054 to put down the heresy
of Berengar of Tours. But the death of Leo recalled him to Italy,](https://image.slidesharecdn.com/46259-250404071409-95dd221f/85/Time-Series-Analysis-Fourth-Edition-George-E-P-Box-31-320.jpg)
![Death of Henry IV.
1106.
Henry V., 1106–
1125.
Philip of France and Robert of Flanders. Henry now declared that his
abdication was forced on him, but offered any terms, compatible
with the possession of the throne, to get absolution from the Pope.
But on 7th August 1106 he died at Liége,
before the real struggle between him and
his son was renewed. The enmity of the Church grudged rest even to
his dead body. The Bishop of Speyer refused to allow the corpse of
the excommunicate to repose beside his ancestors in the stately
church which he himself had built, and for five years it lay in an
unconsecrated chapel.
On 5th January 1106 Henry V. was
crowned for the second time at Mainz. The
first months of his reign were disturbed by his father’s attempt to
regain power. When he was at last undisputed King of Germany, he
found that his cold-blooded treachery had profited him very little.
The Investiture Contest was still unsettled. Between 1103 and 1107
Anselm of Canterbury, restored to his see by William Rufus’ death,
had been carrying on a counterpart of the contest with Henry I. of
England. But the personal animosities which had embittered the
continental struggle were absent, and the dispute did not, as abroad,
involve the larger questions of the whole relations of Church and
State. It was easy, therefore, to settle it by a satisfactory compromise.
Yet at the very moment when Henry had agreed to lay aside
investiture with ring and staff, the envoys of Henry V. were informing
Paschal that their master proposed to insist upon his traditional
rights in the matter. The result was that the continental strife was
renewed with all its old bitterness.
For two years Henry was engaged in wars against Hungary and
Bohemia. In 1110 he resolved to visit Italy to receive the imperial
crown, and to re-establish the old rights of the Empire. Besides a
numerous army, he took with him ‘men of letters able to give reasons
to all comers’ for his acts, among whom was an Irish or Welsh monk
named David, who wrote, at his command, a popular account of how
the king had gone to Rome to extract a blessing from the Pope, as
Jacob had extorted the angel’s blessing.[7]
He found Italy too divided
to offer effectual resistance. The Countess Matilda was old, and
Paschal was no great statesman like Gregory or Urban. Early in 1111
the king’s army approached Rome. The Pope, finding that neither the](https://image.slidesharecdn.com/46259-250404071409-95dd221f/85/Time-Series-Analysis-Fourth-Edition-George-E-P-Box-58-320.jpg)
Time Series Analysis Fourth Edition George E. P. Box
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- 5. Time Series Analysis Fourth Edition George E. P. Box Digital Instant Download Author(s): George E. P. Box, GwilymM. Jenkins, Gregory C. Reinsel(auth.) ISBN(s): 9781118619193, 1118619196 File Details: PDF, 6.95 MB Year: 2008 Language: english
- 7. WILEY SERIES IN PROBABILITY AND STATISTICS Established by WALTER A. SHEWHART and SAMUEL S. WILKS Editors: David J. Balding, Noel A. C. Cressie, Garrett M. Fitzmaurice, Iain M. Johnstone, Geert Molenberghs, David W. Scott, Adrian F. M. Smith, Ruey S. Tsay, Sanford Weisberg Editors Emeriti: Vic Barnett, J. Stuart Hunter, Jozef L. Teugels A complete list of the titles in this series appears at the end of this volume.
- 8. Time Series Analysis Forecasting and Control FOURTH EDITION GEORGE E. P. BOX GWILYM M. JENKINS GREGORY C. REINSEL A JOHN WILEY & SONS, INC., PUBLICATION
- 9. Copyright 2008 by John Wiley & Sons, Inc. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permission. Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visit our web site at www.wiley.com. Library of Congress Cataloging-in-Publication Data: Box, George E. P. Time series analysis : forecasting and control / George E.P. Box, Gwilym M. Jenkins, Gregory C. Reinsel. —4th ed. p. cm. Includes index. ISBN-978-0-470-27284-8 (cloth) 1. Time-series analysis. 2. Predicition theory. 3. Transfer functions. 4. Feedback control systems—Mathematical models. I. Jenkins, Gwilym M. II. Reinsel, Gregory C. III. Title QA280.B67 2008 519.55—dc22 2007044569 Printed in the United States of America 10 9 8 7 6 5 4 3 2 1
- 10. To the memory of Gwilym M. Jenkins Gregory C. Reinsel
- 11. Contents Preface to the Fourth Edition xxi Preface to the Third Edition xxiii 1 Introduction 1 1.1 Five Important Practical Problems, 2 1.1.1 Forecasting Time Series, 2 1.1.2 Estimation of Transfer Functions, 3 1.1.3 Analysis of Effects of Unusual Intervention Events to a System, 4 1.1.4 Analysis of Multivariate Time Series, 5 1.1.5 Discrete Control Systems, 5 1.2 Stochastic and Deterministic Dynamic Mathematical Models, 7 1.2.1 Stationary and Nonstationary Stochastic Models for Forecasting and Control, 7 1.2.2 Transfer Function Models, 12 1.2.3 Models for Discrete Control Systems, 14 1.3 Basic Ideas in Model Building, 16 1.3.1 Parsimony, 16 1.3.2 Iterative Stages in the Selection of a Model, 17 Part One Stochastic Models and Their Forecasting 19 2 Autocorrelation Function and Spectrum of Stationary Processes 21 2.1 Autocorrelation Properties of Stationary Models, 21 2.1.1 Time Series and Stochastic Processes, 21 2.1.2 Stationary Stochastic Processes, 24 vii
- 12. viii CONTENTS 2.1.3 Positive Definiteness and the Autocovariance Matrix, 25 2.1.4 Autocovariance and Autocorrelation Functions, 29 2.1.5 Estimation of Autocovariance and Autocorrelation Functions, 31 2.1.6 Standard Errors of Autocorrelation Estimates, 33 2.2 Spectral Properties of Stationary Models, 35 2.2.1 Periodogram of a Time Series, 35 2.2.2 Analysis of Variance, 37 2.2.3 Spectrum and Spectral Density Function, 38 2.2.4 Simple Examples of Autocorrelation and Spectral Density Functions, 43 2.2.5 Advantages and Disadvantages of the Autocorrelation and Spectral Density Functions, 45 A2.1 Link between the Sample Spectrum and Autocovariance Function Estimate, 45 3 Linear Stationary Models 47 3.1 General Linear Process, 47 3.1.1 Two Equivalent Forms for the Linear Process, 47 3.1.2 Autocovariance Generating Function of a Linear Process, 50 3.1.3 Stationarity and Invertibility Conditions for a Linear Process, 51 3.1.4 Autoregressive and Moving Average Processes, 53 3.2 Autoregressive Processes, 55 3.2.1 Stationarity Conditions for Autoregressive Processes, 55 3.2.2 Autocorrelation Function and Spectrum of Autoregressive Processes, 57 3.2.3 First-Order Autoregressive (Markov) Process, 59 3.2.4 Second-Order Autoregressive Process, 61 3.2.5 Partial Autocorrelation Function, 66 3.2.6 Estimation of the Partial Autocorrelation Function, 69 3.2.7 Standard Errors of Partial Autocorrelation Estimates, 70 3.3 Moving Average Processes, 71
- 13. CONTENTS ix 3.3.1 Invertibility Conditions for Moving Average Processes, 71 3.3.2 Autocorrelation Function and Spectrum of Moving Average Processes, 72 3.3.3 First-Order Moving Average Process, 73 3.3.4 Second-Order Moving Average Process, 75 3.3.5 Duality Between Autoregressive and Moving Average Processes, 78 3.4 Mixed Autoregressive–Moving Average Processes, 79 3.4.1 Stationarity and Invertibility Properties, 79 3.4.2 Autocorrelation Function and Spectrum of Mixed Processes, 80 3.4.3 First-Order Autoregressive–First-Order Moving Average Process, 82 3.4.4 Summary, 86 A3.1 Autocovariances, Autocovariance Generating Function, and Stationarity Conditions for a General Linear Process, 86 A3.2 Recursive Method for Calculating Estimates of Autoregressive Parameters, 89 4 Linear Nonstationary Models 93 4.1 Autoregressive Integrated Moving Average Processes, 93 4.1.1 Nonstationary First-Order Autoregressive Process, 93 4.1.2 General Model for a Nonstationary Process Exhibiting Homogeneity, 95 4.1.3 General Form of the Autoregressive Integrated Moving Average Model, 100 4.2 Three Explicit Forms for The Autoregressive Integrated Moving Average Model, 103 4.2.1 Difference Equation Form of the Model, 103 4.2.2 Random Shock Form of the Model, 104 4.2.3 Inverted Form of the Model, 111 4.3 Integrated Moving Average Processes, 114 4.3.1 Integrated Moving Average Process of Order (0, 1, 1), 115 4.3.2 Integrated Moving Average Process of Order (0, 2, 2), 119 4.3.3 General Integrated Moving Average Process of Order (0, d, q), 123 A4.1 Linear Difference Equations, 125 A4.2 IMA(0, 1, 1) Process with Deterministic Drift, 131
- 14. x CONTENTS A4.3 Arima Processes with Added Noise, 131 A4.3.1 Sum of Two Independent Moving Average Processes, 132 A4.3.2 Effect of Added Noise on the General Model, 133 A4.3.3 Example for an IMA(0, 1, 1) Process with Added White Noise, 134 A4.3.4 Relation between the IMA(0, 1, 1) Process and a Random Walk, 135 A4.3.5 Autocovariance Function of the General Model with Added Correlated Noise, 135 5 Forecasting 137 5.1 Minimum Mean Square Error Forecasts and Their Properties, 137 5.1.1 Derivation of the Minimum Mean Square Error Forecasts, 139 5.1.2 Three Basic Forms for the Forecast, 141 5.2 Calculating and Updating Forecasts, 145 5.2.1 Convenient Format for the Forecasts, 145 5.2.2 Calculation of the ψ Weights, 147 5.2.3 Use of the ψ Weights in Updating the Forecasts, 148 5.2.4 Calculation of the Probability Limits of the Forecasts at Any Lead Time, 150 5.3 Forecast Function and Forecast Weights, 152 5.3.1 Eventual Forecast Function Determined by the Autoregressive Operator, 152 5.3.2 Role of the Moving Average Operator in Fixing the Initial Values, 153 5.3.3 Lead l Forecast Weights, 154 5.4 Examples of Forecast Functions and Their Updating, 157 5.4.1 Forecasting an IMA(0, 1, 1) Process, 157 5.4.2 Forecasting an IMA(0, 2, 2) Process, 160 5.4.3 Forecasting a General IMA(0, d, q) Process, 163 5.4.4 Forecasting Autoregressive Processes, 164 5.4.5 Forecasting a (1, 0, 1) Process, 167 5.4.6 Forecasting a (1, 1, 1) Process, 169
- 15. CONTENTS xi 5.5 Use of State-Space Model Formulation for Exact Forecasting, 170 5.5.1 State-Space Model Representation for the ARIMA Process, 170 5.5.2 Kalman Filtering Relations for Use in Prediction, 171 5.5.3 Smoothing Relations in the State Variable Model, 175 5.6 Summary, 177 A5.1 Correlations Between Forecast Errors, 180 A5.1.1 Autocorrelation Function of Forecast Errors at Different Origins, 180 A5.1.2 Correlation Between Forecast Errors at the Same Origin with Different Lead Times, 182 A5.2 Forecast Weights for Any Lead Time, 182 A5.3 Forecasting in Terms of the General Integrated Form, 185 A5.3.1 General Method of Obtaining the Integrated Form, 185 A5.3.2 Updating the General Integrated Form, 187 A5.3.3 Comparison with the Discounted Least Squares Method, 187 Part Two Stochastic Model Building 193 6 Model Identification 195 6.1 Objectives of Identification, 195 6.1.1 Stages in the Identification Procedure, 195 6.2 Identification Techniques, 196 6.2.1 Use of the Autocorrelation and Partial Autocorrelation Functions in Identification, 196 6.2.2 Standard Errors for Estimated Autocorrelations and Partial Autocorrelations, 198 6.2.3 Identification of Some Actual Time Series, 200 6.2.4 Some Additional Model Identification Tools, 208 6.3 Initial Estimates for the Parameters, 213 6.3.1 Uniqueness of Estimates Obtained from the Autocovariance Function, 213 6.3.2 Initial Estimates for Moving Average Processes, 213 6.3.3 Initial Estimates for Autoregressive Processes, 215
- 16. xii CONTENTS 6.3.4 Initial Estimates for Mixed Autoregressive–Moving Average Processes, 216 6.3.5 Initial Estimate of Error Variance, 218 6.3.6 Approximate Standard Error for w, 218 6.3.7 Choice Between Stationary and Nonstationary Models in Doubtful Cases, 220 6.4 Model Multiplicity, 221 6.4.1 Multiplicity of Autoregressive–Moving Average Models, 221 6.4.2 Multiple Moment Solutions for Moving Average Parameters, 224 6.4.3 Use of the Backward Process to Determine Starting Values, 225 A6.1 Expected Behavior of the Estimated Autocorrelation Function for a Nonstationary Process, 225 A6.2 General Method for Obtaining Initial Estimates of the Parameters of a Mixed Autoregressive–Moving Average Process, 226 7 Model Estimation 231 7.1 Study of the Likelihood and Sum-of-Squares Functions, 231 7.1.1 Likelihood Function, 231 7.1.2 Conditional Likelihood for an ARIMA Process, 232 7.1.3 Choice of Starting Values for Conditional Calculation, 234 7.1.4 Unconditional Likelihood; Sum-of-Squares Function; Least Squares Estimates, 235 7.1.5 General Procedure for Calculating the Unconditional Sum of Squares, 240 7.1.6 Graphical Study of the Sum-of-Squares Function, 245 7.1.7 Description of “Well-Behaved” Estimation Situations; Confidence Regions, 248 7.2 Nonlinear Estimation, 255 7.2.1 General Method of Approach, 255 7.2.2 Numerical Estimates of the Derivatives, 257 7.2.3 Direct Evaluation of the Derivatives, 258 7.2.4 General Least Squares Algorithm for the Conditional Model, 260 7.2.5 Summary of Models Fitted to Series A to F, 263
- 17. CONTENTS xiii 7.2.6 Large-Sample Information Matrices and Covariance Estimates, 264 7.3 Some Estimation Results for Specific Models, 268 7.3.1 Autoregressive Processes, 268 7.3.2 Moving Average Processes, 270 7.3.3 Mixed Processes, 271 7.3.4 Separation of Linear and Nonlinear Components in Estimation, 271 7.3.5 Parameter Redundancy, 273 7.4 Likelihood Function Based on the State-Space Model, 275 7.5 Unit Roots in Arima Models, 280 7.5.1 Formal Tests for Unit Roots in AR Models, 281 7.5.2 Extensions of Unit-Root Testing to Mixed ARIMA Models, 286 7.6 Estimation Using Bayes’s Theorem, 287 7.6.1 Bayes’s Theorem, 287 7.6.2 Bayesian Estimation of Parameters, 289 7.6.3 Autoregressive Processes, 290 7.6.4 Moving Average Processes, 293 7.6.5 Mixed Processes, 294 A7.1 Review of Normal Distribution Theory, 296 A7.1.1 Partitioning of a Positive-Definite Quadratic Form, 296 A7.1.2 Two Useful Integrals, 296 A7.1.3 Normal Distribution, 297 A7.1.4 Student’s t Distribution, 300 A7.2 Review of Linear Least Squares Theory, 303 A7.2.1 Normal Equations and Least Squares, 303 A7.2.2 Estimation of Error Variance, 304 A7.2.3 Covariance Matrix of Least Squares Estimates, 305 A7.2.4 Confidence Regions, 305 A7.2.5 Correlated Errors, 305 A7.3 Exact Likelihood Function for Moving Average and Mixed Processes, 306 A7.4 Exact Likelihood Function for an Autoregressive Process, 314 A7.5 Asymptotic Distribution of Estimators for Autoregressive Models, 323
- 18. xiv CONTENTS A7.6 Examples of the Effect of Parameter Estimation Errors on Variances of Forecast Errors and Probability Limits for Forecasts, 327 A7.7 Special Note on Estimation of Moving Average Parameters, 330 8 Model Diagnostic Checking 333 8.1 Checking the Stochastic Model, 333 8.1.1 General Philosophy, 333 8.1.2 Overfitting, 334 8.2 Diagnostic Checks Applied to Residuals, 335 8.2.1 Autocorrelation Check, 337 8.2.2 Portmanteau Lack-of-Fit Test, 338 8.2.3 Model Inadequacy Arising from Changes in Parameter Values, 343 8.2.4 Score Tests for Model Checking, 344 8.2.5 Cumulative Periodogram Check, 347 8.3 Use of Residuals to Modify the Model, 350 8.3.1 Nature of the Correlations in the Residuals When an Incorrect Model Is Used, 350 8.3.2 Use of Residuals to Modify the Model, 352 9 Seasonal Models 353 9.1 Parsimonious Models for Seasonal Time Series, 353 9.1.1 Fitting versus Forecasting, 353 9.1.2 Seasonal Models Involving Adaptive Sines and Cosines, 354 9.1.3 General Multiplicative Seasonal Model, 356 9.2 Representation of the Airline Data by a Multiplicative (0, 1, 1) × (0, 1, 1)12 Model, 359 9.2.1 Multiplicative (0, 1, 1) ×(0, 1, 1)12 Model, 359 9.2.2 Forecasting, 360 9.2.3 Identification, 367 9.2.4 Estimation, 370 9.2.5 Diagnostic Checking, 375 9.3 Some Aspects of More General Seasonal ARIMA Models, 375 9.3.1 Multiplicative and Nonmultiplicative Models, 375 9.3.2 Identification, 379
- 19. CONTENTS xv 9.3.3 Estimation, 380 9.3.4 Eventual Forecast Functions for Various Seasonal Models, 381 9.3.5 Choice of Transformation, 383 9.4 Structural Component Models and Deterministic Seasonal Components, 384 9.4.1 Structural Component Time Series Models, 384 9.4.2 Deterministic Seasonal and Trend Components and Common Factors, 388 9.4.3 Estimation of Unobserved Components in Structural Models, 390 9.5 Regression Models with Time Series Error Terms, 397 9.5.1 Model Building, Estimation, and Forecasting Procedures for Regression Models, 399 9.5.2 Restricted Maximum Likelihood Estimation for Regression Models, 404 A9.1 Autocovariances for Some Seasonal Models, 407 10 Nonlinear and Long Memory Models 413 10.1 Autoregressive Conditional Heteroscedastic (ARCH) Models, 413 10.1.1 First-Order ARCH Model, 415 10.1.2 Consideration for More General Models, 416 10.1.3 Model Building and Parameter Estimation, 417 10.2 Nonlinear Time Series Models, 420 10.2.1 Classes of Nonlinear Models, 421 10.2.2 Implications and Examples of Nonlinear Models, 424 10.3 Long Memory Time Series Processes, 428 10.3.1 Fractionally Integrated Processes, 429 10.3.2 Estimation of Parameters, 433 Part Three Transfer Function and Multivariate Model Building 437 11 Transfer Function Models 439 11.1 Linear Transfer Function Models, 439 11.1.1 Discrete Transfer Function, 439 11.1.2 Continuous Dynamic Models Represented by Differential Equations, 442
- 20. xvi CONTENTS 11.2 Discrete Dynamic Models Represented by Difference Equations, 447 11.2.1 General Form of the Difference Equation, 447 11.2.2 Nature of the Transfer Function, 449 11.2.3 First- and Second-Order Discrete Transfer Function Models, 450 11.2.4 Recursive Computation of Output for Any Input, 456 11.2.5 Transfer Function Models with Added Noise, 458 11.3 Relation Between Discrete and Continuous Models, 458 11.3.1 Response to a Pulsed Input, 459 11.3.2 Relationships for First- and Second-Order Coincident Systems, 461 11.3.3 Approximating General Continuous Models by Discrete Models, 464 A11.1 Continuous Models with Pulsed Inputs, 465 A11.2 Nonlinear Transfer Functions and Linearization, 470 12 Identification, Fitting, and Checking of Transfer Function Models 473 12.1 Cross-Correlation Function, 474 12.1.1 Properties of the Cross-Covariance and Cross-Correlation Functions, 474 12.1.2 Estimation of the Cross-Covariance and Cross-Correlation Functions, 477 12.1.3 Approximate Standard Errors of Cross-Correlation Estimates, 478 12.2 Identification of Transfer Function Models, 481 12.2.1 Identification of Transfer Function Models by Prewhitening the Input, 483 12.2.2 Example of the Identification of a Transfer Function Model, 484 12.2.3 Identification of the Noise Model, 488 12.2.4 Some General Considerations in Identifying Transfer Function Models, 490 12.3 Fitting and Checking Transfer Function Models, 492 12.3.1 Conditional Sum-of-Squares Function, 492 12.3.2 Nonlinear Estimation, 495 12.3.3 Use of Residuals for Diagnostic Checking, 497 12.3.4 Specific Checks Applied to the Residuals, 498 12.4 Some Examples of Fitting and Checking Transfer Function Models, 501
- 21. CONTENTS xvii 12.4.1 Fitting and Checking of the Gas Furnace Model, 501 12.4.2 Simulated Example with Two Inputs, 507 12.5 Forecasting With Transfer Function Models Using Leading Indicators, 509 12.5.1 Minimum Mean Square Error Forecast, 510 12.5.2 Forecast of CO2 Output from Gas Furnace, 514 12.5.3 Forecast of Nonstationary Sales Data Using a Leading Indicator, 517 12.6 Some Aspects of the Design of Experiments to Estimate Transfer Functions, 519 A12.1 Use of Cross Spectral Analysis for Transfer Function Model Identification, 521 A12.1.1 Identification of Single Input Transfer Function Models, 521 A12.1.2 Identification of Multiple Input Transfer Function Models, 523 A12.2 Choice of Input to Provide Optimal Parameter Estimates, 524 A12.2.1 Design of Optimal Inputs for a Simple System, 524 A12.2.2 Numerical Example, 527 13 Intervention Analysis Models and Outlier Detection 529 13.1 Intervention Analysis Methods, 529 13.1.1 Models for Intervention Analysis, 529 13.1.2 Example of Intervention Analysis, 532 13.1.3 Nature of the MLE for a Simple Level Change Parameter Model, 533 13.2 Outlier Analysis for Time Series, 536 13.2.1 Models for Additive and Innovational Outliers, 537 13.2.2 Estimation of Outlier Effect for Known Timing of the Outlier, 538 13.2.3 Iterative Procedure for Outlier Detection, 540 13.2.4 Examples of Analysis of Outliers, 541 13.3 Estimation for ARMA Models with Missing Values, 543 13.3.1 State-Space Model and Kalman Filter with Missing Values, 544 13.3.2 Estimation of Missing Values of an ARMA Process, 546
- 22. xviii CONTENTS 14 Multivariate Time Series Analysis 551 14.1 Stationary Multivariate Time Series, 552 14.1.1 Covariance Properties of Stationary Multivariate Time Series, 552 14.1.2 Spectral Characteristics for Stationary Multivariate Processes, 554 14.1.3 Linear Filtering Relations for Stationary Multivariate Processes, 555 14.2 Linear Model Representations for Stationary Multivariate Processes, 556 14.2.1 Vector Autoregressive–Moving Average (ARMA) Models and Representations, 557 14.2.2 Aspects of Nonuniqueness and Parameter Identifiability for Vector ARMA Models, 563 14.2.3 Echelon Canonical Form of the Vector ARMA Model, 565 14.2.4 Relation of Vector ARMA to Transfer Function and ARMAX Model Forms, 569 14.3 Nonstationary Vector Autoregressive–Moving Average Models, 570 14.4 Forecasting for Vector Autoregressive–Moving Average Processes, 573 14.4.1 Calculation of Forecasts from ARMA Difference Equation, 573 14.4.2 Forecasts from Infinite MA Form and Properties of Forecast Errors, 575 14.5 State-Space Form of the Vector ARMA Model, 575 14.6 Statistical Analysis of Vector ARMA Models, 578 14.6.1 Initial Model Building and Least Squares for Vector AR Models, 578 14.6.2 Estimation and Model Checking for Vector ARMA Models, 583 14.6.3 Estimation and Inferences for Co-integrated Vector AR Models, 585 14.7 Example of Vector ARMA Modeling, 588 Part Four Design of Discrete Control Schemes 597 15 Aspects of Process Control 599 15.1 Process Monitoring and Process Adjustment, 600 15.1.1 Process Monitoring, 600
- 23. CONTENTS xix 15.1.2 Process Adjustment, 603 15.2 Process Adjustment Using Feedback Control, 604 15.2.1 Feedback Adjustment Chart, 605 15.2.2 Modeling the Feedback Loop, 607 15.2.3 Simple Models for Disturbances and Dynamics, 608 15.2.4 General Minimum Mean Square Error Feedback Control Schemes, 612 15.2.5 Manual Adjustment for Discrete Proportional–Integral Schemes, 615 15.2.6 Complementary Roles of Monitoring and Adjustment, 617 15.3 Excessive Adjustment Sometimes Required by MMSE Control, 620 15.3.1 Constrained Control, 621 15.4 Minimum Cost Control with Fixed Costs of Adjustment and Monitoring, 623 15.4.1 Bounded Adjustment Scheme for Fixed Adjustment Cost, 623 15.4.2 Indirect Approach for Obtaining a Bounded Adjustment Scheme, 625 15.4.3 Inclusion of the Cost of Monitoring, 627 15.5 Feedforward Control, 627 15.5.1 Feedforward Control to Minimize Mean Square Error at the Output, 629 15.5.2 An Example—Control of the Specific Gravity of an Intermediate Product, 632 15.5.3 Feedforward Control with Multiple Inputs, 635 15.5.4 Feedforward–Feedback Control, 636 15.5.5 Advantages and Disadvantages of Feedforward and Feedback Control, 638 15.5.6 Remarks on Fitting Transfer Function–Noise Models Using Operating Data, 639 15.6 Monitoring Values of Parameters of Forecasting and Feedback Adjustment Schemes, 642 A15.1 Feedback Control Schemes Where the Adjustment Variance is Restricted, 644 A15.1.1 Derivation of Optimal Adjustment, 644 A15.2 Choice of the Sampling Interval, 653 A15.2.1 Illustration of the Effect of Reducing Sampling Frequency, 654 A15.2.2 Sampling an IMA(0, 1, 1) Process, 654
- 24. xx CONTENTS Part Five Charts and Tables 659 Collection of Tables and Charts 661 Collection of Time Series Used for Examples in the Text and in Exercises 669 References 685 Part Six Exercises and Problems 701 Index 729
- 25. Preface to the Fourth Edition It may be of interest to briefly recount how this book came to be written. Gwilym Jenkins and I first became friends in the late 1950s. We were intrigued by an idea that a chemical reactor could be designed that optimized itself automatically and could follow a moving maximum. We both believed that many advances in statistical theory came about as a result of interaction with researchers who were working on real scientific problems. Helping to design and build such a reactor would present an opportunity to further demonstrate this concept. When Gwilym Jenkins came to visit Madison for a year, we discussed the idea with the famous chemical engineer Olaf Hougen, then in his eighties. He was enthusiastic and suggested that we form a small team in a joint project to build such a system. The National Science Foundation later supported this project. It took three years, but suffice it to say, that after many experiments, several setbacks, and some successes the reactor was built and it worked. As expected this investigation taught us a lot. In particular we acquired profi- ciency in the manipulation of difference equations that were needed to characterize the dynamics of the system. It also gave us a better understanding of nonstationary time series required for realistic modeling of system noise. This was a happy time. We were doing what we most enjoyed doing: interacting with experimenters in the evolution of ideas and the solution of real problems, with real apparatus and real data. Later there was fallout in other contexts, for example, advances in time series analysis, in forecasting for business and economics, and also developments in statistical process control (SPC) using some notions learned from the engineers. Originally Gwilym came for a year. After that I spent each summer with him in England at his home in Lancaster. For the rest of the year, we corresponded using small reel-to-reel tape recorders. We wrote a number of technical reports and published some papers but eventually realized we needed a book. The first two editions of this book were written during a period in which Gwilym was, with extraordinary courage, fighting a debilitating illness to which he succumbed sometime after the book had been completed. Later Gregory Reinsel, who had profound knowledge of the subject, helped to complete the third edition. Also in this fourth edition, produced after his untimely xxi
- 26. Discovering Diverse Content Through Random Scribd Documents
- 27. Foundation of Aversa, 1030. The sons of Tancred of Hauteville. Conquest of Apulia, 1041–2. 1022 [see page 50], he found his chief obstacle in the new Greek fortress of Troja, obstinately defended by some valiant Normans in the pay of their old foe the Catapan. Other Normans now flocked to the land of promise. Among these was a chieftain named Ranulf, who joined Sergius, Prince of Naples, a vassal of the Greeks, in his war against the Lombard prince Pandulf of Capua. In reward for his services Ranulf received one of the richest districts of the Terra di Lavoro, where he built in 1030 a town named Aversa, the first Norman settlement in Italy. This foundation makes a new departure in Norman policy. The Normans no longer came to Italy as isolated adventurers willing to sell their swords to the highest bidder. By much the same arts as those by which their brethren later got hold of the fairest parts of Wales and Ireland, the adventurers strove to carve feudal states for themselves out of the chaos of southern Italy. Whilst cleverly utilising the feuds that raged around them, they pursued their interests with such dexterity, courage, and clear- headed selfishness, that brilliant success soon crowned their efforts. Conrad II. sojourned at Capua in 1038, deposed Pandulf and confirmed Ranulf in the possession of Aversa, which he erected into a county owing homage to the Western Emperor. Three of the twelve sons of the Norman lord, Tancred of Hauteville, now left their scanty patrimony in the Côtentin and joined the Normans in Italy. Their names were William of the Iron Arm, Drogo, and Humphrey. In 1038 they joined the Greeks under George Maniaces in an attempt to expel the Mohammedans from Sicily. Messina and Syracuse were captured, but an affront to their companion-in-arms Ardouin drove the Normans back to the mainland in the moment of victory, and led them to wreak their vengeance on the Greeks by a strange compound of violence and treachery. Ardouin their friend took the Greek pay and became governor of Melfi, the key of Apulia. He proposed to the Normans that he should deliver Melfi to them, and make that a starting-point for the conquest of Apulia, which he proposed to divide between them and himself. The northerners accepted his proposals. In 1041 Melfi was delivered into their hands, and a long war broke out between them and their former allies. By shrewdly putting Adenulfus, the Lombard Duke of Benevento at the head of their
- 28. Robert Guiscard. Leo IX. turns against the Normans. armies, the Normans got allies that were probably necessary in the early years of the struggle. But they were soon strong enough to repudiate their associate. The divisions of the Greeks further facilitated their task. In 1042 William of the Iron Arm was proclaimed lord of the Normans of Apulia, with Melfi as the centre of his power. In 1046 William of Apulia died, and Drogo, his brother, succeeded him. Henry III., then in Italy, recognised Drogo as Count of Apulia, while renewing the grant of Aversa to another Ranulf. He also urged the Normans to drive out of Benevento the Lombards, who after the spread of the Norman power were making common cause with the Greeks. About this time a fourth son of Tancred of Hauteville came to Italy, where he soon made himself the hero of the Norman conquerors. Anna Comnena, the literary daughter of the Emperor Alexius, describes Robert Guiscard as he appeared to his enemies. ‘His high stature excelled that of the most mighty warriors. His complexion was ruddy, his hair fair, his shoulders broad, his eyes flashed fire. It is said that his voice was like the voice of a whole multitude, and could put to flight an army of sixty thousand men.’ A poor gentleman’s son, Robert was consumed by ambition to do great deeds, and joined to great bravery and strength an extraordinary subtlety of spirit. His surname of Guiscard is thought to testify to his ability and craft. Badly received by his brothers in Apulia, he was reduced to taking service with the Prince of Capua against his rival of Salerno. Events soon gave him an opportunity of striking a blow for himself. Meanwhile, a formidable combination was forming against the Normans. Argyrus, son of Meles, had deserted his father’s policy and came from Constantinople, as Patrician and Catapan (Governor), with special commissions from the Emperor. Unable to persuade the Normans to take service with the Emperor against the Persians, he soon waged war openly against them, and procured the murder of Count Drogo in 1051, but was soon driven to take refuge in Bari. Meanwhile Leo IX. had become Pope, and his all-absorbing curiosity had led him to two journeys into southern Italy, where he persuaded the inhabitants of Benevento to accept the protection of the Holy See against the dreaded Northmen. It looked as if the
- 29. Battle of Civitate, 1053. Peace between the Normans and the Pope. Eastern and Western Empires were likely to combine with the Papacy and the Lombards to get rid of the restless adventurers. In 1052 Henry III. granted the duchy of Benevento to the Roman Church, and Leo hurried from Hungary to southern Italy to enforce his claims on his new possession. In May 1053 Leo IX. reached Monte Casino. There soon flocked round him a motley army, drawn together from every district of central and southern Italy and eager to uphold the Holy Father against the Norman usurpers; but the few hundred Germans, who had followed the Pope over the Alps, were probably more serviceable in the field than the mixed multitude of Italians. The Normans, abandoned by their allies, united all their scanty forces for a decisive struggle. The armies met on 18th June near Civitate (Civitella) on the banks of the Fortore, the place of the first Norman victory in Italy. The longhaired and gigantic Germans affected to despise their diminutive Norman foes, and the fiercest fight was fought between the Pope’s fellow- countrymen and Humphrey of Hauteville, the new Count of Apulia, who commanded the Norman right. There the Norman horse long sought in vain to break up the serried phalanx of the German infantry. But the left and centre of the Normans, led respectively by Richard, the new Count of Aversa, and Robert Guiscard, easily scattered the enemies before them, and, returning in good time from the pursuit, enabled Humphrey to win a final victory over the Germans. Leo IX. barely escaped with his liberty from the fatal field. Peter Damiani and the zealots denounced him for his unseemly participation in acts of violence, and the object which had induced him to depart from his sacred calling had been altogether unfulfilled. He retired to Benevento, where he soon came to an understanding with the Normans, giving them his apostolic blessing and absolving them from their blood-guiltiness. Even in the moment of victory the Normans had shown every respect to the head of the Church, and self-interest now combined with enthusiasm to make them his friends. But Leo entered into no formal treaty with them. He remained at Benevento, carefully watching their movements and corresponding with Constantine Monomachus in the hope of renewing the league against them. But his dealings with the Greek Empire soon broke down owing to the theological differences which
- 30. Victor II., 1054– 1057. Henry III.’s last visit to Italy, 1055. Position of the Countess Matilda. the acute hostility of Leo and Michael Cærularius now brought to a head. Leo gave up all hope of western help when he fulminated the excommunication against Cærularius, which led at once to the final split of Catholic and Orthodox. In the spring of 1054 he returned to Rome and died. His exploits and holy life had given him a great reputation for holiness, and he was canonised as a saint. Even the disaster of Civitate and the eastern schism did little to diminish his glory. Leo IX.’s successor as Pope was another German, Gebhard, bishop of Eichstädt, who took the name of Victor II. (1054–1057). He continued to work on the lines of Pope Leo, though more in the spirit of a politician. During Victor’s pontificate, Henry III. made his second and last visit to Italy (1055). His presence was highly necessary. His strongest Italian enemy, the powerful Marquis Boniface of Tuscany, was dead, leaving an only daughter Matilda heiress of his great inheritance. Boniface’s widow Beatrice soon found a second husband in Godfrey the Bearded, Duke of Lower Lorraine, the chief enemy of Henry in Germany. In this union there was a danger of the German and Italian opposition to the Empire being combined. But the formidable league dissolved at once on Henry’s appearance. Godfrey fled from Italy, and Beatrice and her daughter were led into honourable captivity in Germany. Godfrey’s brother Frederick, hitherto a scheming ecclesiastic, renounced the world, and became one of the most zealous of the monks of Monte Casino. But the death of the Emperor and the long minority that followed, soon restored the power of the heiress of Boniface. The Countess Matilda, powerful alike in Tuscany and north of the Apennines, became the most zealous of the allies of the Papacy. Her support gave that material assistance without which the purely spiritual aims of the Papacy could hardly prevail. At the moment when the Papacy had permanently absorbed the teachings of Cluny, it was a matter of no small moment that the greatest temporal power of middle Italy was on its side. It was a solid compensation for Leo’s failure against the Normans.
- 31. Hildebrand’s early career and character. We have now come to one of the real crises of history. The new spirit had gained ascendency at Rome, and the great man had arisen who was to present the papal ideal with all the authority of genius. Hildebrand of Soana[6] was the son of a well-to-do Tuscan peasant; he had been brought up by his uncle, abbot of the strict convent of St. Mary’s on the Aventine, which was the centre of the Cluniac ideas in Rome, and where he made his profession as monk. He became the chaplain of Gregory VI. who, though he bought the Papacy with gold, had striven his best to carry out the work of reformation. When deprived of his office at Sutri, Gregory VI. had been compelled to retire to Germany with the Emperor. Hildebrand, now about twenty-five years old, accompanied his master in his exile. In 1048 the deposed Pope died, and his chaplain betook himself to Cluny, where he remained for a full year, and where, he tells us, he would have gladly spent the rest of his life. But in 1049 Leo IX. passed through Cluny on his way to Rome, and Hildebrand was commanded to accompany him. With his return to Rome his active career began. As papal sub-deacon he reorganised the crippled finances of the Holy See, and strengthened the hold of the Pope over the unruly citizens. As papal legate he was sent to France in 1054 to put down the heresy of Berengar of Tours. But the death of Leo recalled him to Italy,
- 32. Stephen IX., 1057– 1058. Nicholas II., 1058– 1061. whence he went to the Emperor at the head of the deputation that successfully requested the appointment of Victor II. With this Pope he was as powerful as with Leo. But Victor II. died in 1057, and Frederick of Lorraine left his newly-won abbot’s chair at Monte Casino to ascend the throne of St. Peter as Stephen IX. Though a zealot for the ideas of Cluny, Stephen, as the head of the house of Lorraine, was the natural leader of the political opposition to the imperial house both in Germany and Italy. He made Peter Damiani a cardinal, and zealously pushed forward the warfare against simony in Germany. Stephen’s early death in 1058, when Hildebrand was away in Germany, brought about a new crisis. The Counts of Tusculum thought the moment opportune to make a desperate effort to win back their old influence. They terrorised Rome with their troops, and brought about the irregular election of one of the Crescentii, who called himself Benedict X. The prompt action of Hildebrand preserved the Papacy for the reforming party. He hurried back to Florence, and formed a close alliance with Duke Godfrey of Lorraine, Stephen’s brother, against the nominee of Tusculum. The stricter cardinals met at Siena and chose Gerhard, Bishop of Florence, a Burgundian by birth, as orthodox Pope. Gerhard held another synod at Sutri, where the Antipope was formally deposed. Early in 1059 he entered Rome in triumph. By assuming the name of Nicholas II., he proclaimed himself the successor of the most successful and aggressive of Popes. As Archdeacon of Rome, Hildebrand acted as chief minister to the Pope whom he had made. Henceforth till his death he dominated the papal policy. While previous reformers had sought salvation by calling the Emperor over the Alps, Hildebrand had found in Duke Godfrey and his wife champions as effective for his purpose on Italian soil. With the establishment of Pope Nicholas, through the arms of Godfrey and Matilda, the imperial alliance ceases to become a physical necessity to the reforming party in Italy. Hildebrand had won for the Church her freedom. Before long he began to aim at domination. Nicholas II. ruled as Pope from 1058 to 1061. Within those few years, three events were brought about which enormously strengthened the position of the Papacy, already possessed of a great moral force by its permanent identification with the reforming party,
- 33. Lateran Synod and reform in Papal elections, 1059. The Normans become the vassals of the Pope, 1059. and the final abasement of the unworthy local factions, that had so long aspired to wield its resources. These events were the settlement of the method of papal elections, the establishment of a close alliance between the Papacy and the Normans of southern Italy, and the subjection of Lombardy to the papal authority. In 1059 Nicholas held a synod in the Lateran which drew up the famous decree that set aside the vague ancient rights of the Roman clergy and people to choose their bishop, in favour of the close corporation of the College of Cardinals. The decree was drawn up in studiously vague language, but put the prerogative voice into the very limited circle of the seven cardinal bishops of the suburbicarian dioceses. These were to add to themselves the cardinal priests and deacons, whose assent was regarded as including that of clergy and people at large. A Roman clerk was to be preferred if worthy, and Rome was to be the ordinary place of election; but, if difficulties intervened, any person could be chosen, and any place made the seat of election. The due rights of King Henry and his successors to confirm their choice were reserved, but in terms that suggested a special personal favour granted of his own goodwill by the Pope to a crowned Emperor, rather than the recognition of an immemorial legal right. The decree did not, as was hoped, save the Church from schisms like those of Benedict X. Neither was the pre- eminence of the suburbicarian bishops permanently maintained. But henceforth the legal right of the cardinals to be the electors of future Popes became substantially uncontested. It is not likely that this involved any real change of practice. But in embodying custom in a formal shape it gave subsequent efforts to set up Antipopes the condemnation of illegality, and so stood the Papacy in good stead in the troubles that were soon to ensue. The council also witnessed the abject degradation of the Antipope and the recantation of the heretic Berengar of Tours. In the years that followed the battle of Civitate, the Normans had steadily extended their power over Apulia and Calabria. But the south of Italy is so rugged and mountainous that even the bravest of warriors could only win their way slowly. In 1057 the valiant Count Humphrey died, leaving his sons so young that he
- 34. Roger of Hauteville. Synod of Melfi. Robert, Duke of Apulia; and Richard, Duke of Capua. had been constrained to beg his brother Robert to act as their protector. But the barons of Apulia insisted that Robert should be their count in full succession to Humphrey. Soon after Roger of Hauteville, the youngest of the twelve sons of Tancred, left the paternal roof to share the fortune of his brothers. ‘He was,’ says Geoffrey of Malaterra, ‘a fine young man, of lofty stature and elegant proportions. Very eloquent in speech, wise in counsel, and gifted with extraordinary foresight, he was gay and affable to all, and so strong and valiant that he soon gained the good graces of every one.’ Robert Guiscard received Roger in a more brotherly spirit than had been shown on his own first arrival by Drogo and Humphrey. He gave him a sufficient following of troops and sent him to Calabria, where he soon established himself as lord of half the district, though under his brother’s overlordship. Meanwhile, Richard of Aversa had driven out the Lombards from Capua and added it to his dominions. The Normans were still, however, not free from danger from the Popes. Victor II. had disapproved of Leo IX.’s policy, yet before his death he had become their enemy. Stephen IX. formed various projects against them. But Hildebrand now turned Nicholas II. to wiser counsels. In 1059 Hildebrand went in person to Capua and concluded a treaty with Count Richard, who, as the ally of the monks of Monte Casino, was the most friendly of the Norman chieftains to the Church. Almost immediately the archdeacon returned to Rome with a strong Norman escort, and soon after a Norman army spread terror among the partisans of the Antipope. In the summer of 1059 Nicholas himself held a synod in Melfi, the Apulian capital, where he passed canons condemning married priests. After the formal session was over, the Pope made Robert Guiscard Duke of Apulia and Calabria, and ‘future Duke’ of Sicily, if he should ever have the good luck to drive out the infidels. In return Robert, ‘Duke by the grace of God and of St. Peter,’ agreed to hold his lands as the Pope’s vassal, paying an annual rent of twelve pence for each ploughland. Richard of Capua, either then or earlier, took the same oath. Thus the famous alliance between the Normans and the Papacy was consummated, which by uniting the strongest military power in Italy to the papal policy, enabled the Holy See to wield the temporal
- 35. The Patarini in Lombardy. Milan submits to Rome. Alexander II. 1061– 1073. with almost as much effect as the spiritual sword. Thus the Papacy assumed a feudal suzerainty over southern Italy which outlasted the Middle Ages. Within seven years of the Synod of Melfi, the establishment of the Norman duke William the Bastard in England, as the ally of the Pope, still further bound the most restless, active, and enterprising race in Europe to the apostolic see. The Pope now intervened decisively in the long struggle between the traditional and the strict parties in Lombardy, where the ancient independence of the archbishops of Milan had long been assailed by the Patarini or rag-pickers, as the reformers were contemptuously called. Lovers of old ways in the north, with the Archbishop Guido of Milan at their head, had long upheld clerical marriage as the ancient custom of the Church of St. Ambrose. Peter Damiani was now sent as papal legate to Milan to uphold the ‘rag-bags’ in their struggle. At a synod held in Milan, the zealous monk made short work of the married clerks and of the immemorial rights of the archbishop. Guido proffered an abject submission and received a contemptuous restitution of his archbishopric. The continuance of the friendship of Godfrey and Matilda secured middle Italy, as the alliance with Normans and Patarini had secured the south and the north. The strongest princes of Gaul and Burgundy were on the zealots’ side. The imperialist prelates of Germany, headed by Anno of Cologne, made a faint effort to stem the tide, but the decrees fulminated by German synods against Nicholas and his work were unknown or disregarded in Italy. The untimely death of Nicholas in no wise altered the course of events. The next Pope, Alexander II., was Anselm, Bishop of Lucca, who had shared with Peter Damiani in the victory over the simoniacs and married clerks in Lombardy. His appointment by the cardinals without the least reference to King Henry IV. gave the greatest offence in Germany, and brought to a head the growing tension between Empire and Papacy. A synod at Basel declared Pope Alexander’s election invalid, and set up an Antipope, Cadalus, Bishop of Parma, who had been the real soul of the opposition to the Patarini in Lombardy. Honorius II. (this was the name he assumed) hurried over the Alps, and in 1062 was strong enough, with the help of the Counts of Tusculum, to fight
- 36. Later triumphs of Robert Guiscard, 1068–1085. an even battle with Alexander’s partisans, and for a time to get possession of St. Peter’s. But the factions that controlled the government of the young Henry IV. could not unite even in upholding an Antipope, while the religious enthusiasm, which the reforming movement had evoked, was ardently on the side of Alexander. Condemned by Anno of Cologne and his party in Germany, Honorius was rejected in 1064 by a council at Mantua. Nevertheless, he managed to live unmolested and with some supporters until his own death in 1072. His successful rival Alexander only outlived him a year. It was then time for the archdeacon himself to assume the responsible leadership of the movement which he had so long controlled. In 1073 Hildebrand became Pope Gregory VII. The reconciliation with the Papacy stood the Normans in good stead. Henceforth they posed as the champions of Western Catholicism against Eastern Orthodoxy and Islam. Though the Norman chieftains still wrangled hotly with each other, the tide in south Italy had definitely turned in their favour. In 1071 the capture of Bari, after a three years’ siege, finally expelled the Greeks from Italy. The Lombard principality of Salerno was also absorbed, and the greater part of the territories of the dukes of Benevento, save the city and its neighbourhood, which Robert Guiscard, much to his own disgust, was forced to yield to his papal suzerain. We shall see in other chapters how Robert crossed the Straits of Otranto and aspired to conquer the Greek Empire, how he came to the help of Gregory VII. in his greatest need, and how his son Bohemund took part in the first Crusade and founded the principality of Antioch. When Robert died in 1085, all southern Italy acknowledged him as its lord, save the rival Norman principality of Capua, the half-Greek republics of Amalfi and Naples, and the papal possession of Benevento. While Robert Guiscard was thus consolidating his power in the peninsula, an even harder task was being accomplished by his younger brother Roger, sometimes in alliance, and sometimes in fierce hostility with the Duke of Apulia. The grant of Nicholas II. had contemplated the extension of the Norman rule to Sicily. The divisions of the Mohammedan world had cut off the island from the Caliphate of the Fatimites, and its independent Ameers were hardly equal to the task of ruling the island and keeping in order a timid but
- 37. Roger’s conquest of Sicily, 1060–1101. The feudalisation of Naples and Sicily. refractory population of Christian serfs. The increasing power of Robert was fatal to the independence of Roger in Calabria, and he gladly accepted the invitation of the discontented Christians of Messina to deliver them from the bondage of the infidel. In 1060 Roger led his first expedition to Sicily, which was unsuccessful. But early next year he came again, and this time the dissensions of the Mohammedans in Sicily enabled him to have friends among Saracens as well as Christians. In the summer of 1061 Robert came to his help. Messina was easily captured, and proved invaluable as the starting-point of later expeditions. The infidels were badly beaten at the battle of Castrogiovanni, and before the end of the year the standards of Roger had waved as far west as Girgenti. The first successes were not quite followed up. In 1064 the Normans were forced to raise the siege of Palermo. The compact Mussulman population of Western Sicily opposed a very different sort of resistance to the invaders from that which they had experienced in the Christian East. But the process of conquest was resumed after the capture of Bari had given Robert leisure to come to his brother’s help. In 1072 Palermo was taken by the two brothers jointly. Robert claimed the lion’s share of the spoil. Roger, forced to yield him the suzerainty of the whole island, and a great domain under his direct rule, including Palermo and Messina, threw himself with untiring zeal into the conquest of the parts of the island that still adhered to Islam. Thirty years after his first expedition, the last Saracens were expelled from the rocky fastnesses of the western coasts, and the inaccessible uplands of the interior. The Normans took with them to Italy their language, their manners, their art, and above all, their polity. On the ruins of the Greek, Lombard and Saracen power, the Normans feudalised southern Italy so thoroughly that the feudalism of Naples and Sicily long outlasted the more indigenous feudalism of Tuscany or Romagna. Freed from his grasping brother’s tutelage after 1085, Roger ruled over Sicily as count till his death in 1101. We shall see how his son united Sicily with Apulia in a single sovereignty, which has in various shapes endured as the kingdom of Naples or Sicily, until the establishment of a united Italy in our own days.
- 39. GENEALOGY OF THE HOUSE OF TANCRED OF HAUTEVILLE.
- 40. The minority of Henry IV., 1056– 1072. Regency of the Empress Agnes, 1056–1062. CHAPTER VI THE INVESTITURE CONTEST (1056–1125) Minority of Henry IV.—Regency of Agnes—Rivalry of Adalbert and Anno—The Saxon Revolt—Election of Gregory VII.—Beginnings of the Investiture Contest—Canossa and its results—Rudolf of Swabia and Guibert of Ravenna—The Normans and Gregory VII. —Victor III. and Urban II.—Last years of Henry IV.—Henry V. and Pascal II.—Calixtus II. and the Concordat of Worms—Death of Henry V. While the Cluniac movement had at last attained ascendency over the best minds of Europe, and a swarm of monastic reformers had prepared the way for the great revival of spiritual religion and hierarchical pretensions; while in Italy strong papalist powers, like the Countess Matilda and the Normans of the south, had arisen to menace the imperial authority, the long minority of Henry IV. sapped the personal influence of Cæsar over Italy and brought about a lengthened period of faction and weak rule in Germany. On Henry III.’s death, his son, Henry IV., was a boy of six. The great Emperor’s power secured the child’s undisputed succession, but was too personal, too military in its character to prove any safeguard against the dangers of a long minority. Nor did the choice of ruler during Henry IV.’s nonage improve the state of affairs. Henry III.’s widow, Agnes of Poitou, a pious well-meaning lady, acted as regent for her son, but her weakness of will and inconsistency of conduct gave full scope to discontented nobles ready to take advantage of a woman’s sway. The lay nobles availed themselves of her helplessness to plunder and despoil the
- 41. Abduction of Henry by Anno of Cologne, 1062. Rivalry of Adalbert of Bremen and Anno of Cologne, 1065–1070. prelates, while they complained that Agnes neglected their counsels for those of low-born courtiers and personal favourites. After six years of confusion the Empress was driven from power. Anno, Archbishop of Cologne, a vigorous, experienced, and zealous prelate, full of ambition and violence, joined himself with Otto of Nordheim, the newly appointed Duke of Bavaria, Count Egbert of Brunswick, and some of the bishops, in a well-contrived plot to get possession of the young king. In May 1062 the three chief conspirators visited the king at his palace of Saint Suitbert’s, situated on an island in the Rhine, some miles below Düsseldorf, now called Kaiserswerth. One day after dinner Anno persuaded the boy king to inspect an elaborately-fitted-up barge. As soon as Henry had entered the boat, the oarsmen put off and rowed away. Henry was soon frightened and plunged into the water, but Count Egbert leapt in and rescued him. The king was pacified by flattery and taken to Cologne. The crowd cried shame on the treachery of the bishop, but Henry remained in his custody, and Agnes made no serious attempt to regain her authority, but reconciled herself with Anno and retired into a monastery. Anno proposed to the magnates that the regency should be exercised by the bishop of the diocese in which the king happened to be staying. By carefully selecting the king’s places of abode, he thus secured the reality of power without its odium. By throwing over the Antipope he procured the support of the Hildebrandine party, and was likened by Peter Damiani to another Jehoiada. But his pride and arrogance soon raised him up enemies; and young Henry, who never forgave his abduction, bitterly resented his tutelage. Adalbert, Archbishop of Bremen, took the lead among Anno’s enemies. He was a man of high birth, great experience, and unbounded ambition, an old confidant of Henry III., and filled with a great scheme for making his archbishopric a permanent patriarchate over the infant churches of Scandinavia. He made himself personally attractive to the king, who contrasted his kindness and indulgence with the austerity of Anno. By Adalbert’s influence Henry was declared of age to govern on attaining his fifteenth year in 1065. Henceforth Adalbert disposed of all the high offices in Church and State, and growing more greedy as he became more successful, excited much ill-will among the religious
- 42. by plundering the monasteries right and left. He appropriated to himself the two great abbeys of Lorsch and Corvey, and sought in vain to propitiate his enemies by allowing other magnates, including even his rival Anno, to similarly despoil other monasteries. The king was made so poor that he hardly had enough to live on. But Adalbert at least sought to continue the great traditions of statecraft of Henry III., and showed more policy and skill than the crowd of bishops who had previously shared power with Anno. At last, in 1066, the nobles combined against Adalbert at a Diet at Tribur, and Henry was roundly told that he must either dismiss Adalbert or resign his throne. Adalbert retired to his diocese, and Anno and Otto of Nordheim again had the chief control of affairs. But neither party could rule with energy or spirit, and Henry, now nearly grown up, showed no decided capacity to make things better. The young king was tall, dignified, and handsome. He was affable and kindly to men of low rank, with whom he was ever popular, though he could be stern and haughty to the magnates, whose power he feared. He had plenty of spirit and fair ability. But he had been brought up so laxly by Archbishop Adalbert that he was headstrong, irresolute, profligate, and utterly deficient in self-control. He never formulated a policy, and if he championed great causes, he did so blindly and in ignorance. Married to Bertha, daughter of the Marquis Odo of Turin, in 1065, he gave offence both to her powerful kinsfolk and to the strict churchmen by refusing to live with her, and talking of a divorce. He had now to put down open rebellions. In 1069 the Margrave Dedi strove to rouse the Thuringians to revolt, and in 1070 Otto of Bavaria, the most important of the dukes surviving, after the death of Duke Godfrey of Lorraine in the previous year, was driven into rebellion. So divided were the German nobles, so helpless the German king, that instead of ruling the Italians, there seemed every prospect of the Italians ruling them. In 1069 Peter Damiani went to Germany as legate, and compelled Henry to reconcile himself with Bertha. Peter was horrified at the unblushing simony of the German bishops, and, on his report, Anno of Cologne and several other of the greatest prelates of Germany were summoned to Rome and thoroughly humiliated. Anno atoned for his laxity by his edifying discharge of the meanest monastic duties in his own great foundation at Siegburg, but his influence was gone and his political career was at an end. His fall brought Adalbert back to some of his
- 43. The Saxon Revolt, 1073–1075. ancient influence. The death of the Archbishop of Bremen in 1072 unloosed the last link that connected the new reign with the old traditions. Henry IV.’s reign now really began. A thorough Swabian, his favourite ministers were Swabians of no high degree, and he had no faith in the goodwill or loyalty of the men of the north. He had kept vacant the Saxon dukedom. On every hill-top of Saxony and Thuringia he built strong castles, whose lawless garrisons plundered and outraged the peasantry. There was ever fierce ill-will between northern and southern Germany during the Middle Ages. The policy of the southern Emperor soon filled the north with anger, and the Saxon nobles prepared for armed resistance. In 1073 Henry fitted out an expedition, whose professed destination was against the Poles. It was believed in Saxony that his real object was to subdue the Saxons and hand them over to the Swabians. Accordingly in the summer of 1073 a general Saxon revolt broke out, headed by the natural leaders of Saxony both in Church and State, including the Archbishop of Magdeburg, the deposed Duke Otto of Bavaria, and the fierce Margrave Dedi, already an unsuccessful rebel. The insurgents demanded the instant demolition of the castles, the dismissal of Henry’s evil counsellors, and the restitution of their lands that he had violently seized. On receiving no answer they shut up Henry in the strong castle of Harzburg, whence he escaped with the utmost difficulty to the friendly cloister of Hersfeld. In the course of the summer the rebels destroyed many of the new castles. The levies summoned for the Polish campaign refused to turn their arms against the Saxons, and Henry saw himself powerless amidst the general falling away. A meeting at Gerstungen, where Henry’s friends strove to mediate with the rebels, led to a suggestion that the king should be deposed. Only at Worms and in the Swabian cities did Henry receive any real support. He gathered together a small army and strove to fight a winter campaign against the Saxons, but failed so completely that he was forced to accept their terms. However, hostilities were renewed in 1075, when Henry won a considerable victory at Hohenburg on the Unstrut, and forced the Saxons to make an unconditional submission. Otto of Nordheim, the Archbishop of Magdeburg, and the other leaders were imprisoned. On the ruins of Saxon liberty Henry now aspired to build up a despotism.
- 44. Election of Gregory VII. 1073. His character and policy. Hildebrand was now Pope. During the funeral service of Alexander II. at St. John’s in the Lateran, a great shout arose from the multitude in the church that Hildebrand should be their bishop. The cardinal, Hugh the White, addressed the assembly. ‘You know, brethren,’ he said, ‘how, since the time of Leo IX., Hildebrand has exalted the Roman Church, and freed our city. We cannot find a better Pope than he. Indeed, we cannot find his equal. Let us then elect him, who, having been ordained in our church, is known to us all, and thoroughly approved by us.’ There was the great shout in answer: ‘Saint Peter has chosen Hildebrand to be Pope!’ Despite his resistance, Hildebrand was dragged to the church of St. Peter ad Vincula, and immediately enthroned. The cardinals had no mind to upset this irregular election, strangely contrary though it was to the provisions of Nicholas II. The German bishops, alarmed at Hildebrand’s reputation for severity, urged the king to quash the appointment, but Henry contented himself with sending to Rome to inquire into the circumstances of the election. Hildebrand showed great moderation, and actually postponed his consecration until Henry’s consent had been obtained. This Henry had no wish to withhold. On 29th June 1073 Hildebrand was hallowed bishop. By assuming the name of Gregory VII., he proclaimed to the world the invalidity of the deposition of his old master at the Synod of Sutri. The wonderful self-control which the new Pope had shown so long did not desert him in his new position. Physically, there was little to denote the mighty mind within his puny body. He was of low stature, shortlegged and corpulent. He spoke with a stammer, and his dull complexion was only lighted up by his glittering eyes. He was not a man of much learning or originality, and contributed little towards the theory of the papal or sacerdotal power. But he was one of the greatest practical men of the Middle Ages; and his single-minded wish to do what was right betokened a dignity of moral nature that was rare indeed in the eleventh century. His power over men’s minds was enormous, even to their own despite. The fierce and fanatical Peter Damiani called him his ‘holy Satan.’ ‘Thy will,’ said he, ‘has ever been a command to me—evil but lawful. Would that I had always served God and St. Peter as faithfully as I have served thee.’ Even as archdeacon he assumed so great a state, and lived in such constant
- 45. intercourse with the world, that monastic zealots like Damiani were scandalised, and some moderns have questioned (though groundlessly) whether he was ever a professed monk at all. Profoundly convinced of the truth of the Cluniac doctrines, he showed a fierce and almost unscrupulous statecraft in realising them that filled even Cluny with alarm. His ideal was to reform the world by establishing a sort of universal monarchy for the Papacy. He saw all round him that kings and princes were powerless for good, but mighty for evil. He saw churchmen living greedy and corrupt lives for want of higher direction and control. Looking at a world distraught by feudal anarchy, his ambition was to restore the ‘peace of God,’ civilisation, and order, by submitting the Church to the Papacy, and the world to the Church. ‘Human pride,’ he wrote, ‘has created the power of kings; God’s mercy has created the power of bishops. The Pope is the master of Emperors. He is rendered holy by the merits of his predecessor, St. Peter. The Roman Church has never erred, and Holy Scripture proves that it never can err. To resist it is to resist God.’ For the next twelve years he strove with all his might to make his power felt throughout Christendom. Sometimes his enthusiasm caused him to advance claims that even his best friends would not admit, as when William the Conqueror was constrained to repudiate the Holy See’s claims of feudal sovereignty over England, which, after similar pretensions had been recognised by the Normans in Sicily, Gregory and his successors were prone to assert whenever opportunity offered. The remotest parts of Europe felt the weight of his influence. But the intense conviction of the righteousness of his aims, that made compromise seem to him treason to the truth, did something to detract from the success of his statecraft. He was too absolute, too rigid, too obstinate, too extreme to play his part with entire advantage to himself and his cause. Yet with all his defects there is no grander figure in history. Gregory realised the magnitude of his task, but he never shrank from it. ‘I would that you knew,’ wrote he to the Abbot of Cluny, ‘the anguish that assails my soul. The Church of the East has gone astray from the Catholic faith. If I look to the west, the north, or the south, I find but few bishops whose appointments and whose lives are in accordance with the laws of the Church, or who govern God’s people through love and not through worldly ambition. Among princes I know not one who sets the honour of God before his own, or justice
- 46. The Synod of 1075, and the attack on Simony and Lay Investiture. The beginnings of the Investiture Contest, 1075. before gain. If I did not hope that I could be of use to the Church, I would not remain at Rome a day.’ From the very first he was beset on every side with difficulties. Even the alliance with the Normans was uncertain. Robert Guiscard, with his brother Roger, waged war against Gregory’s faithful vassal, Richard of Capua; and Robert, who threatened the papal possession of Benevento, went so far that he incurred excommunication. Philip of France, ‘the worst of the tyrants who enslaved the Church,’ had to be threatened with interdict. A project to unite the Eastern with the Western Church broke down lamentably. A contest with Henry IV. soon became inevitable. But Gregory abated nothing of his high claims. In February 1075 he held a synod at Rome, at which severe decrees against simony and the marriage of clerks were issued. The practice of lay investiture, by which secular princes were wont to grant bishoprics and abbeys by the conferring of spiritual symbols such as the ring and staff, had long been regarded by the Cluniacs as the most glaring of temporal aggressions against the spiritual power. This practice was now sternly forbidden. ‘If any one,’ declared the synod, ‘henceforth receive from the hand of any lay person a bishopric or abbey, let him not be considered as abbot or bishop, and let the favour of St. Peter and the gate of the Church be forbidden to him. If an emperor, a king, a duke, a count, or any other lay person presume to give investiture of any ecclesiastical dignity, let him be excommunicated.’ This decree gave the signal for the great Investiture Contest, and for the greater struggle of Papacy and Empire that convulsed Europe, save during occasional breaks, for the next two centuries. Up to the issue of the decree as to investitures, the relation between Gregory and Henry IV. had not been unfriendly. Henry had admitted that he had not always respected the rights of the Church, but had promised amendment for the future. But to give up investitures would have been to change the whole imperial system of government. He was now freed, by his victory at Hohenburg, from the Saxon revolt. The German bishops, afraid of the Pope’s strictness, encouraged his resistance, and even in Italy he had many partisans. The Patarini were driven out of Milan, and Henry scrupled not to invest a new archbishop with the see of St. Ambrose. Even at
- 47. Council at Worms, 1076. Vatican Synod, 1076. Weakness of Henry’s position in Germany. Rome, Gregory barely escaped assassination while celebrating mass. In January 1076 Henry summoned a German council to Worms. Strange and incredible crimes were freely attributed to the Pope, and the majority of the German bishops pronounced him deposed. Henry himself wrote in strange terms to the Pope: ‘Henry, king not by usurpation but by God’s grace, to Hildebrand, henceforth no pope but false monk,— Christ has called us to our kingdom, while He has never called thee to the priesthood. Thou hast attacked me, a consecrated king, who cannot be judged but by God Himself. Condemned by our bishops and by ourselves, come down from the place that thou hast usurped. Let the see of St. Peter be held by another, who will not seek to cover violence under the cloak of religion, and who will teach the wholesome doctrine of St. Peter. I, Henry, king by the grace of God, with all of my bishops, say unto thee—“Come down, come down.”’ In February 1076 Gregory held a great synod in the Vatican, at which the Empress Agnes was present, with a great multitude of Italian and French bishops. A clerk from Parma named Roland delivered the king’s letter to the Pope before the council. There was a great tumult, and Roland would have atoned for his boldness with his life but for the Pope’s personal intervention. Henry was now formally excommunicated and deposed. ‘Blessed Peter,’ declared Gregory, ‘thou and the Mother of God and all the saints are witness that the Roman Church has called upon me to govern it in my own despite. As thy representative I have received from God the power to bind and to loose in Heaven and on earth. For the honour and security of thy Church, in the Name of God Almighty, I prohibit Henry the king, son of Henry the Emperor, who has risen with unheard-of pride against thy Church, from ruling Germany and Italy. I release all Christians from the oaths of fealty they may have taken to him, and I order that no one shall obey him.’ War was thus declared between Pope and king. Though the position of both parties was sufficiently precarious, Henry was at the moment in the worst position for carrying on an internecine combat. He could count very little on the support of his German subjects. Those who most feared the Pope were the self-seekers and
- 48. Diet of Tribur, 1076. Humiliation of Henry. Henry’s winter journey through the simoniacs, whose energy was small and whose loyalty less. The saints and the zealots were all against him. The Saxons profited by his embarrassments to renew their revolt, and soon chased his garrisons out of their land. The secular nobles, who saw in his policy the beginnings of an attempt at despotism, held aloof from his court. It was to no purpose that Henry answered the anathemas of Gregory with denunciations equally unmeasured, and complained that Gregory had striven to unite in his hands both the spiritual and the temporal swords, that God had kept asunder. Hermann, Bishop of Metz, the Pope’s legate in Germany, ably united the forces against him. At last, the nobles and bishops of Germany gathered together on 16th October 1076 at Tribur, where the papal legates were treated with marked deference, though Henry took up his quarters at Oppenheim, on the other bank of the Rhine, afraid to trust himself amidst his disaffected subjects. Henry soon saw that he had no alternative but submission. The magnates were so suspicious of him that it needed the personal intercession of Hugh, Abbot of Cluny, to prevail upon them to make terms with him at all. Finally a provisional agreement was patched up, upon conditions excessively humiliating to Henry. The barons refused to obey him until he had obtained absolution from the Pope, who, moreover, had promised to go to Germany in person and hold a council in the succeeding February. Pending this, Henry was to remain at Speyer without kingly revenue, power, or dignity, and still shut off by his excommunication from the offices of the Church. If Henry could not satisfy the Pope in February, he was to be regarded as deposed. Abandoned by Germany, Henry abode some two months at Speyer, gloomily anticipating the certain ruin to his cause that would follow the Pope’s appearance in a German council. He realised that he could do nothing unless he reconciled himself to Gregory; and, hearing good news of his prospects in northern Italy, thought that his best course was to betake himself over the Alps, where the Pope might well prove less rigorous, if he found him at the head of a formidable band of Italian partisans. It was a winter of extraordinary severity, but any risks were better than inglorious inaction at Speyer. Accordingly Henry broke his compact with his nobles, and towards the end of
- 49. Burgundy and Lombardy, 1076– 77. Canossa, Jan. 1077. December secretly set out on his journey southward. He was accompanied by Bertha and his little son, but only one German noble was included among his scanty following. He traversed Burgundy, and kept his miserable Christmas feast at Besançon. Thence crossing the Mont Cenis at the risk of his life, he appeared early in the new year amidst his Lombard partisans at Pavia. But though urged to take up arms, Henry feared the risks of a new and doubtful struggle. Germany could only be won back by submission. He resolved to seek out the Pope and throw himself on his mercy. Gregory was then some fifteen miles south of Reggio, at an impregnable mountain stronghold belonging to the Countess Matilda, called Canossa, which crowned one of the northern spurs of the Apennines, and overlooked the great plain. He had sought the protection of its walls as a safe refuge against the threatened Lombard attack which Henry, it was believed, had come over the Alps to arrange. The Countess Matilda and Hugh of Cluny, Henry’s godfather, were with the Pope, and many of the simoniac bishops of Germany had already gone to Canossa and won absolution by submission. On 21st January 1077 Henry left his wife and followers at Reggio, and climbed the steep snow-clad road that led to the mountain fastness. Gregory refused to receive him, but he had interviews with Matilda and his godfather in a chapel at the foot of the castle-rock, and induced them to intercede with the Pope on his behalf. Gregory would hear of nothing but complete and unconditional submission. ‘If he be truly penitent, let him surrender his crown and insignia of royalty into our hands, and confess himself unworthy of the name and honour of king.’ But the pressure of the countess and abbot at last prevailed upon him to be content with abject contrition without actual abandonment of his royal state. For three days Henry waited in the snow outside the inner gate of the castle-yard, barefoot, fasting, and in the garb of a penitent. On the fourth day the Pope consented to admit him into his presence. With the cry ‘Holy father, spare me!’ the king threw himself at the Pope’s feet. Gregory raised him up, absolved him, entertained him at his table, and sent him away with much good advice and his blessing. But the terms of Henry’s reconciliation were sufficiently hard. He was to promise to submit himself to the judgment of the German magnates, presided over by
- 50. Results of Canossa. Diet of Forchheim, March 1077. Rudolf of Swabia, Anti-Cæsar. the Pope, with respect to the long catalogue of charges brought against him. Until that was done he was to abstain from the royal insignia and the royal functions. He was to be prepared to accept or retain his crown according to the judgment of the Pope as to his guilt or innocence. He was, if proved innocent, to obey the Pope in all things pertaining to the Church. If he broke any of these conditions, another king was to be forthwith elected. The humiliation of Henry at Canossa is so dramatic and so famous an event that it is hard to realise that it was but an incident in the midst of a long struggle. It settled nothing, and profited neither Henry nor Gregory. Gregory found that his harshness had to some extent alienated that public opinion on which the Papacy depended almost entirely for its influence. Henry found that his submission had not won over his German enemies, but had thoroughly disgusted the anti-papal party in northern Italy, upon which alone he could count for armed support. The Lombards now talked of deposing the cowardly monarch in favour of his little son. But the future course of events rested after all upon the action of the German nobles, who held their Diet at Forchheim in March 1077. To this assembly Henry was not even invited; and for the present he preferred remaining in Italy. The Pope also did not appear in person, but was represented by two legates. The old charges against Henry were brought up once more, and the legates expressed their wonder that the patient Germans had submitted so long to be ruled by such a monster. Without giving Henry the least opportunity of refuting the accusations, it was determined to proceed at once to the choice of a new king. The suffrages of the magnates fell on Duke Rudolf of Swabia. Before his appointment, Rudolf was compelled to renounce all hereditary claim to the throne on behalf of his heirs, and to allow freedom of election to all bishoprics. He was then crowned at Mainz by Archbishop Siegfried. The news of Rudolf’s election at once brought Henry back over the Alps. He soon found that he now had devoted partisans in the land that had rejected him when he was under the ban of the Pope. He was warmly welcomed in Bavaria, in Burgundy, and especially in the great towns of the Rhineland, always faithful to the imperial cause.
- 51. Civil war between Rudolf and Henry, 1077–1080. Battle of Flarchheim, 1080. Renewed excommunication and deposition of Henry, March 1080. Guibert of Ravenna elected Antipope, June 1080. Rudolf’s own duchy of Swabia rejected its duke in favour of the prince who had ever loved the Swabians. Rebel Saxony was alone strongly on Rudolf’s side. Even the Pope could not make up his mind to ratify the action of his legates and accept Rudolf as king. For more than two years civil war raged between Rudolf and Henry. It was substantially a continuation of the Saxon revolt. At last, in January 1080, a decisive battle was fought at Flarchheim on the banks of the Unstrut, in which Henry was utterly defeated. During all this time Gregory had contented himself with offers of arbitration. Though Henry practised lay investiture as freely as ever, it was not until after his defeat that the Pope once more declared himself against him. Yielding to the indignant remonstrances of Rudolf and the Saxons, he convoked a synod at Rome in March 1080, where he renewed Henry’s excommunication, and again deprived him of his kingdoms of Germany and Italy. ‘Act so,’ said Gregory to the assembled prelates, ‘that the world shall know that ye who have power to bind and to loose in heaven, can grant or withhold kingdoms, principalities, and other possessions according to each man’s merits. And if you are fit to judge in things spiritual, ought ye not to be deemed competent to judge in things temporal?’ Rudolf was now recognised as king, and another universal prohibition of lay investitures was issued. Gregory boasted that, before the next feast of SS. Peter and Paul, Henry would have lost his throne and his life. But each fresh aggression of the Pope increased his rival’s power. Henry now showed an energy and vigour that contrasted strangely with his spiritless action three years before. Both in Germany and Italy he found himself supported by partisans as enthusiastic as those of the Pope. The bishops of Germany declared for him, and the old foes of the Pope in Italy took courage to continue the contest. In June Henry met at Brixen the German and Italian bishops who adhered to his side. This assembly declared Gregory deposed and excommunicate, and elected Guibert, Archbishop of Ravenna as his successor.
- 52. Battle on the Elster, and death of Rudolf, 15th October 1080. Hermann of Luxemburg, Anti- Cæsar. Henry’s visit to Italy, 1081. War between Henry and Gregory, 1081–1084. The new Antipope had in his youth served Henry III., and, as chancellor of Italy, had striven to uphold the imperial authority during Henry IV.’s minority. He had once been on friendly terms with Gregory, but had quarrelled with him, and had for some time been the soul of the imperialist party in north Italy. He was of high birth, unblemished character, great abilities, and long experience. He assumed the title of Clement III., and at once returned to Ravenna to push matters to extremities against Gregory. The rash violence of the Pope had been answered with equal violence by his enemies. There were two Popes and two Emperors. The sword alone could decide between them. Fortune favoured Henry and Clement both in Germany and Italy. On 15th October 1080 a great battle was fought on the banks of the Elster, not far from the later battlefields of Lützen. The fierce assault of Otto of Nordheim changed what threatened to be a Saxon defeat into a brilliant victory for the northern army. But Rudolf of Swabia was slain, and the victorious Saxons wasted their opportunity while they quarrelled as to his successor. It was nearly a year before they could agree upon Hermann of Luxemburg as their new king. Before this the back of the revolt had been broken, and Henry, secure of Germany, had once more gone to Italy. Crossing the Brenner in March 1081, he went on progress through the Lombard cities, and abode with Pope Clement at Ravenna. Thence he set out for Rome, meeting little resistance on his way save from the Countess Matilda. The Normans of Naples, on whose help Gregory had counted, made no effort to protect their suzerain. In May Henry celebrated the Whitsun feast outside the walls of Rome. Gregory did not lose his courage even with the enemy at his gate. The Romans were faithful to him, and Henry, who saw no chance of besieging the great city successfully, was forced to retreat northwards by the feverish heat of summer. He retired to Lombardy, where his position was unassailable. Next year he was back again before the walls of Rome, but the occupation of Tivoli was his
- 53. Coronation of Henry by Guibert, 1084. The Normans come to Gregory’s help, 1084. Sack of Rome. Death of Gregory in exile, 1085. greatest success. In 1083 a third attack gave him possession of the Leonine city, but even in this extremity Gregory would listen to no talk of conciliation. ‘Let the king lay down his crown and make atonement to the Church,’ was his answer to those who besought him to come to terms. In the early months of 1084 Henry invaded Apulia and kept in check the Normans, who at last were making a show of helping the Pope. In March he appeared for the fourth time before Rome. This time the Romans opened their gates, and Gregory was closely besieged in the castle of St. Angelo. A synod was hastily summoned, which renewed his deposition and excommunication. On Palm Sunday, 1084, Guibert was enthroned, and on Easter Day he crowned Henry Emperor at St. Peter’s. Gregory sent from the castle of St. Angelo an urgent appeal for help to Robert Guiscard. During the troubles of the last few years, Robert’s obligations to his suzerain had weighed very lightly upon him, but Henry’s invasion of Apulia and the certain ruin of the Normans in Naples if the Pope succumbed, at last brought him to decided action. Hastily abandoning his Greek campaign, Robert crossed over to Italy, and in May advanced to the walls of Rome with a large and motley army, in which the Saracens of Sicily were a prominent element. Henry, who had no force sufficient to resist, quitted Rome, and soon crossed the Alps. The Romans tried in vain to defend their city from the Normans. After a four days’ siege treason opened the gates. Rome was ruthlessly sacked, whole quarters were burned down, hideous massacres and outrages were perpetrated, and thousands of Romans were sold as slaves. The Normans then marched home. Gregory could not remain in the desolate city, and followed them to Salerno. The Antipope kept his Christmas amid the ruins of Rome, but soon abandoned the city for his old home at Ravenna. Gregory now fell sick at Salerno. The few faithful cardinals strove to console him by dwelling on the great work which he had accomplished. ‘I set no store by what I have done,’ was his answer. ‘One thing only fills me with hope. I have always loved the law of God and hated iniquity. Therefore I die in exile.’ He passed away on 25th May 1085. Less than two months afterwards, Robert Guiscard died at Corfu.
- 54. Victor III., 1086– 1087. Urban II., 1088– 1099. Henry revisits Italy, 1090. For a year after Gregory’s death, the Papacy remained vacant. At last, in May 1086, the cardinals, profiting by the Antipope’s return to Ravenna, met at Rome and forced the Papacy on the unwilling Desiderius, Abbot of Monte Casino. The new Pope (who assumed the name of Victor III.), was a close friend of Gregory’s and strongly attached to his ideals. But he was too old and too weak to take up Hildebrand’s task, and three days after his election he strove to avoid the troublesome dignity by flight to Monte Casino. Next year he was with difficulty prevailed upon to return to Rome to receive the tiara. But the partisans of the Emperor and of the Countess Matilda fought fiercely for the possession of Rome, and Victor again retreated to his monastery, where death ended his troubles three days after his return (16th September 1087). Next time the cardinals fixed upon a Pope of sterner stuff. Driven from Rome by the Antipope, they made their election at Terracina on 12th March 1088. Their choice fell upon the son of a baron of Champagne named Odo, who had lived long at Cluny as monk and sub-prior, and then served the Roman Court as cardinal-bishop of Ostia. Urban II. (this was the title he took) was a man of ability and force of character, as ardent as Hildebrand for the Cluniac ideals, but more careful of his means of enforcing them than the uncompromising Gregory. He made closer his alliance with the Normans, and, thanks to the help of Duke Roger, Robert Guiscard’s son and successor, was able to return to Rome and remain there for some months. But the troops of the Antipope still held the castle of St. Angelo, and Urban soon found it prudent to retire. He mainly spent the first years of his pontificate in southern Italy under Roger’s protection. Meanwhile, papalists and imperialists fought hard in northern Italy. Germany was now tolerably quiet, and Henry could now devote his chief energies to Italy, which he revisited in 1090. But Urban united the German with the Italian opposition to the Emperor by bringing about a politic marriage between the Countess Matilda and the young son of Welf or Guelf, Duke of Bavaria, the Emperor’s most powerful adversary in Germany. Despite this combination, Henry’s Italian campaigns between 1090 and 1092 were extraordinarily successful. Matilda’s dominions in the plain country were overrun,
- 55. Conrad of Franconia, Anti- Cæsar, 1093. Urban’s Councils at Piacenza and Clermont, 1095. The proclamation of the First Crusade, 1095. and her towns and castles captured. But she held her own in her strongholds in the Apennines, rejected all compromise, and prepared to fight to the last. Henry met his first check when he was driven back in disgrace from an attempted siege of Canossa. The papalists were much encouraged by Henry’s defeat. Soon after they persuaded his son Conrad, a weak and headstrong youth, to rise in revolt against his father. Half Lombardy fell away from father to son. Before the year was out, Conrad received the Iron Crown at Milan, and Urban ventured back to Rome. Worse was to follow. Henry’s second wife, Praxedis of Russia (Bertha had died in 1087), escaped from the prison to which her husband had consigned her, and taking refuge with the Countess Matilda, gave to the world a story of wrongs and outrages that destroyed the last shreds of the Emperor’s reputation. In high glee at the progress of his cause, Urban set out on a lengthened progress that reminds us of the memorable tours of Leo IX. After a long stay in Tuscany, he crossed the Apennines early in 1095, and held a great synod at Piacenza, at which the laws against simony and married clerks were renewed, while the Empress publicly declared her charges against Henry, and ambassadors from the Eastern Emperor pleaded for help, against the growing power of the Seljukian Turks. In the summer Urban crossed the Alps, and remained for more than a year in France and Burgundy, being everywhere received with extraordinary reverence. In November 1095 he held a largely attended synod at Clermont in Auvergne. Not content with his quarrel with the Emperor, he here fulminated excommunication against Philip I. of France, on account of his adultery with Bertrada, Countess of Anjou. But the famous work of the Council of Clermont was the proclamation of the First Crusade. Nothing shows more clearly the strength and nature of the papal power than that this greatest result of the universal monarchy of the Church should have been brought about at a time when all the chief kings of Europe were open enemies of the Papacy. Henry IV. was an old foe, Philip of France had been deliberately attacked, and William Rufus of England was indifferent or hostile. But in the eleventh century the power of even the strongest kings counted for very little. What made the success of Urban’s endeavour
- 56. Urban’s return to Italy, 1096. Henry abandons Italy, 1097. Urban II. in southern Italy, 1098. Synod at Bari. was the appeal to the swarm of small feudal chieftains, who really governed Europe, and to the fierce and undisciplined enthusiasm of the common people, with whom the ultimate strength of the Church really lay. Flushed with his success at Clermont, Urban recrossed the Alps in September 1096. Bands of Crusaders, hastening to the East, mingled with the papal train as he again traversed northern Italy. Rome itself now opened its gates to the homeless lord of the Church. In 1097 Henry IV. abandoned Italy in despair. He restored the elder Welf to the Bavarian duchy, and easily persuaded the younger Welf to quit his elderly bride, and resume his allegiance to the Emperor. Conrad was deprived of the succession, and his younger brother Henry crowned king at Aachen on taking an oath that he would not presume to exercise royal power while his father was alive. Urban was now triumphant, save that his Norman allies were once more giving him trouble, and the castle of St. Angelo was still held for the Antipope. He accordingly again visited southern Italy, and won over Count Roger of Sicily, by conceding the famous privilege to Roger and his heirs that no papal legate should be sent into their lands without their consent, but that the lords of Sicily should themselves act as legates within their dominions. In October 1098 the Pope held a synod at Bari, restored to Catholicism by the Norman conquest in 1071. There, with a view to facilitating the Crusade, the great point of difference between the Eastern and Western Churches—the Procession of the Holy Ghost—was debated at length. Among the prelates attending the council was Anselm of Canterbury, exiled for upholding against William Rufus the principles which Urban had asserted against the Emperor and the King of France. Urban, who had been politic enough not to raise up a third great king against him by supporting Anselm, atoned for past neglect by the deference he now showed to the ‘Pope of the second world.’ As the council broke up, the good news came that the castle of St. Angelo had at last been captured. Urban returned to Rome and devoted himself to the work of the Crusade. On 29th July 1099 he died suddenly. It was his glory
- 57. Death of Urban II., 1099. Death of Conrad, 1101. Paschal II., 1099– 1118. Revolt of the young King Henry, 1104. that the struggle of Pope and Emperor, which had absorbed all the energies of Gregory VII., sank during his pontificate into a second place. Though he abandoned no claim that Gregory had made, he had the good fortune to be able to put himself at the head of crusading Europe, while his opponent shrank into powerless contempt. Next year the Antipope followed Urban to the grave. With Clement, the schism as a real force died. Three short-lived Antipopes pretended to carry on his succession until the death of the Emperor, but no one took them seriously. With the flight of the last pretender in 1106, formal ecclesiastical unity was again restored. Driven out of Italy by his rebel son, Henry IV. found Germany equally indisposed to obey him. Both north and south of the Alps, the real gainers in the long struggle had been the feudal chieftains, and Germany, like Italy, was ceasing to be a single state at all. In 1101 the rebellious Conrad died at Florence, bitterly regretting his treason. Henry’s main object now was to restore peace to Germany, and to effect a reconciliation with the Church. But the new Pope, Paschal II. (Rainerius of Bieda, near Viterbo, elected August 1099), renewed his excommunication, and was as unbending as his predecessors. Before long Paschal was able to extend his intrigues into Germany, and in 1104 the young King Henry raised the Saxons in revolt against his father, and was recognised as king by the Pope. But the Emperor had no spirit left for a fresh contest. At Coblenz he threw himself at his son’s feet, begging only that his own child should not be the instrument of God’s vengeance on his sins. The young king asked for forgiveness, and promised to give up his claims when his father was reconciled with the Church. The Emperor trustfully disbanded his soldiers, and was promptly shut up in prison by his twice-perjured son. On 31st December 1105 he formally abdicated at Ingelheim, and abjectly confessed his offences against the Church. He was told that absolution could only come from the Pope in person, and that it was a boon that he was allowed his personal freedom. He fled from Ingelheim to Cologne, where the goodwill of the citizens showed him that he still had friends. From Cologne he went to Aachen, and from thence to Liége, whose bishop, Otbert, supported him. The Duke of Lorraine declared himself for him, and help was expected from
- 58. Death of Henry IV. 1106. Henry V., 1106– 1125. Philip of France and Robert of Flanders. Henry now declared that his abdication was forced on him, but offered any terms, compatible with the possession of the throne, to get absolution from the Pope. But on 7th August 1106 he died at Liége, before the real struggle between him and his son was renewed. The enmity of the Church grudged rest even to his dead body. The Bishop of Speyer refused to allow the corpse of the excommunicate to repose beside his ancestors in the stately church which he himself had built, and for five years it lay in an unconsecrated chapel. On 5th January 1106 Henry V. was crowned for the second time at Mainz. The first months of his reign were disturbed by his father’s attempt to regain power. When he was at last undisputed King of Germany, he found that his cold-blooded treachery had profited him very little. The Investiture Contest was still unsettled. Between 1103 and 1107 Anselm of Canterbury, restored to his see by William Rufus’ death, had been carrying on a counterpart of the contest with Henry I. of England. But the personal animosities which had embittered the continental struggle were absent, and the dispute did not, as abroad, involve the larger questions of the whole relations of Church and State. It was easy, therefore, to settle it by a satisfactory compromise. Yet at the very moment when Henry had agreed to lay aside investiture with ring and staff, the envoys of Henry V. were informing Paschal that their master proposed to insist upon his traditional rights in the matter. The result was that the continental strife was renewed with all its old bitterness. For two years Henry was engaged in wars against Hungary and Bohemia. In 1110 he resolved to visit Italy to receive the imperial crown, and to re-establish the old rights of the Empire. Besides a numerous army, he took with him ‘men of letters able to give reasons to all comers’ for his acts, among whom was an Irish or Welsh monk named David, who wrote, at his command, a popular account of how the king had gone to Rome to extract a blessing from the Pope, as Jacob had extorted the angel’s blessing.[7] He found Italy too divided to offer effectual resistance. The Countess Matilda was old, and Paschal was no great statesman like Gregory or Urban. Early in 1111 the king’s army approached Rome. The Pope, finding that neither the
- 59. Henry’s Roman journey. Paschal renounces the Temporalities of the Church, 1111. Tumult at Henry’s Coronation. Triumph of Henry over Paschal. Romans nor the Normans would help him, sent to Sutri to make terms. Even in his supreme distress he would not give up freedom of elections or abate his hostility to lay investitures; but he offered that if the king would accept those cardinal conditions he would renounce for the Church all its feudal and secular property. It was a bold or rash attempt to save the spiritual rights of the Church by abandoning its temporalities, lands, and jurisdictions. Henry naturally accepted an offer which put the whole landed estates of the Church at his disposal, and reduced churchmen to live on tithes and offerings— their spiritual sources of revenue. Only the temporalities of the Roman see were to be excepted from this sweeping surrender. On Sunday, 12th February, St. Peter’s church was crowded to witness the hallowing of the Emperor by the Pope. Before the ceremony began the compact was read, and the Pope renounced in the plainest language all intervention in secular affairs, as incompatible with the spiritual character of the clergy. A violent tumult at once arose. German and Italian bishops united to protest vigorously against the light-heartedness with which the Pope gave away their property and jurisdictions, while carefully safeguarding his own. The congregation dissolved into a brawling throng. The clergy were maltreated, and the sacred vessels stolen. The coronation was impossible. The king laid violent hands on Pope and cardinals, and the mob in the streets murdered any Germans whom they happened to come across. After three days of wild turmoil, Henry quitted the city, taking his prisoners with him. After a short captivity, Paschal stooped to obtain his liberty by allowing Henry to exercise investitures and appoint bishops at his will. ‘For the peace and liberty of the Church,’ was his halting excuse, ‘I am compelled to do what I would never have done to save my own life.’ In return Henry promised to be a faithful son of the Church. On 13th April Paschal crowned Henry with maimed rites and little ceremony at St. Peter’s. Canossa was at last revenged. Henry returned in triumph over the Alps, and solemnly interred his father’s remains in holy ground at Speyer. Henry’s triumph made a deep impression on Europe. The blundering Pope had
- 60. Paschal repudiates his concessions. Conspiracies against Henry in Germany. Death of the Countess Matilda, 1115, and of Paschal II., 1118. betrayed the temporal possessions of the clergy, and the necessary bulwarks of the freedom of the spiritual power. The event showed that there were practical limits even to papal infallibility. Paschal was as powerless to retreat from the position of Hildebrand, as he had been to renounce the lands of all prelates but himself. The clergy would not accept the papal decision. In France a movement to declare the Pope a heretic was only stayed by the canonist Ivo of Chartres declaring that the Pope, having acted under compulsion, was not bound to keep his promise. The Italians gladly accepted this way out of the difficulty. Paschal solemnly repudiated his compact. ‘I accept,’ he declared, ‘the decrees of my master, Pope Gregory, and of Urban of blessed memory; that which they have applauded I applaud, that which they have granted I grant, that which they have condemned I condemn.’ Even in Germany Henry found that he had gained nothing by his degradation of the Pope. The air was thick with plots and conspiracies. His most trusted councillors became leaders of treason. Adalbert, Archbishop of Mainz, his chief minister, formed a plot against him and was imprisoned. The Saxons rose once more in revolt under their new Duke Lothair of Supplinburg. Friesland refused to pay tribute. Cologne rose under its Archbishop, and Henry found that he was quite unable to besiege it successfully. The nobles who attended his wedding with Matilda of England at Mainz, profited by the meeting to weave new plots. Next year the citizens of Mainz shut up the Emperor in his palace while he was holding a Diet, and forced him to release their Archbishop. Affairs in Italy were even more gloomy. In 1115 the Countess Matilda died, leaving all her vast possessions to the Holy See. If this will had been carried out, Paschal would have become the greatest temporal power in Italy. Henry therefore crossed the Alps in 1116, anxious, if not to save Matilda’s allodial lands, to take possession of the fiefs of the Empire which she had held. In 1117 Henry occupied Rome and crowned his young English wife Matilda. Even in his exile Paschal had not learnt the
- 61. Gelasius II. (1118– 1119). The Antipope Burdinus. Calixtus II. (1119– 1124). Negotiations for a settlement. lesson of firmness. He died early in 1118, before he had even definitely made up his mind to excommunicate Henry. The new Pope, John of Gaeta, a monk of Monte Casino, who took the name of Gelasius II., was forced to flee from Rome as the Emperor was entering it. Henry now took the decisive step of appointing a Pope of his own. Burdinus, Archbishop of Braga, was in some fashion chosen by a few cardinals, and took the name of Gregory VIII. Gelasius at once excommunicated both Antipope and Emperor. He soon managed to get back to Rome, whence, however, he was again expelled by the malignity of local faction rather than the influence of the Emperor. He now betook himself to Marseilles by sea, and, after a triumphant progress through Provence and Burgundy, held a synod at Vienne. On his way thence to Cluny he was smitten with pleurisy, reaching the monastery with difficulty, and dying there on 18th January 1119. Guy, the high-born Archbishop of Vienne, was chosen somewhat irregularly by the cardinals who had followed Gelasius to Cluny. He had long been conspicuous as one of the ablest upholders of Hildebrandine ideas in the dark days of Paschal II. The son of William the Great, Count of imperial Burgundy (Franche-Comté), he was the kinsman of half the sovereigns of Europe. He was, moreover, a secular (the first Pope not a monk since Alexander II.), and accustomed to diplomacy and statecraft. He resolved to make an effort to heal the investiture strife, and with that object summoned a council to meet at Reims. Henry himself was tired of the struggle. He practically dropped his Antipope, and gave a patient hearing to the agents of the Pope, who came to meet him at Strasburg. These were Hugh, Abbot of Cluny, and the famous theologian, William of Champeaux, now Bishop of Châlons. The two divines pointed out to Henry that the King of France, who did not employ investiture, had as complete a hold over his bishops as the Emperor, and that his father-in-law, Henry of England, who had yielded the point, was still lord over his feudal vassals, whether clerks or laymen. For the first time perhaps, the subject was discussed between the two parties in a reasonable and conciliatory spirit. Before the king and the divines parted, it was
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