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This document discusses various forecasting techniques including: naive forecasting models, smoothing techniques like moving averages, decomposition techniques, exponential smoothing models like Holt's two-parameter method, and Winter's three parameter exponential smoothing model. It also discusses error measurement techniques, time series components, autocorrelation, autoregression, and index number techniques like simple index numbers, weighted and unweighted aggregate price indexes, and the Laspeyres and Paasche price indexes.
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- 1. BY: Devyani Jain (09310) Madhu Vuppuluri (09314) Malvika Bahety (09315) Saloni Grover (09328) Utpala (09337) Vasudha Gupta (09340)
- 2. MeasurementofForecasting error Mean error Mean absolute deviation MAD= mean of absolute value of errors Mean square error MSE= mean of squared errors Mean percentage error Mena absolute percentage error Mean absolute deviation Mean square error Error of an individual forecast= actual value- forecast value Time series components •Trend •Cyclicality •Seasonality •Irregularity
- 4. Linear Regression Trend Analysis 𝑌𝑖 = β0 + β1 + ϵi Regression Trend Analysis Using Quadratic Models Yi = β0 + β1Xti + β2X²ti + ϵi Holt’s Two-Parameter Exponential Smoothing Method
- 5. Decomposition Technique Uses the multiplicative model Multiplicative Model=T.C.S.I Winter’s three parameter exponential smoothing model Uses a weight for seasonality Develops forecasts that include a smoothing value for observations, a trend value and a seasonal value Seasonal effects are patterns of data behaviour that occur in periods of time of less than 1 year.
- 6. Autocorelation Definition: When error terms of regression forecasting model are limited. Problem: Coefficients of regression may not have minimum variance and may be inefficient. Solutions: Adding important predictor variables that have been left out. Transforming data into variables that may help solving the problem Autoregression A multiple regression when independent variable are time lagged version of dependent variable. 𝑦 = 𝑏0 + 𝑏1 𝑌𝑡−1 + 𝑏2 𝑌𝑡−2 + 𝑏3 𝑌𝑡−2
- 7. SIMPLE INDEX NUMBERS Makes possible conversion of prices, costs, quantities etc. for different time periods into a no. scale with base year equaling 100% Ii = Xi/Xo UNWEIGHTED AGGREGATE PRICE INDEX NUMBERS This is a technique used for combining several items and determining index no. for total (aggregate) Ii = ƩPi/ƩPo WEIGHTED AGGREGATE PRICE INDEX NUMBERS Computed by multiplying quantity weights and item prices in determining the market base worth for a given year IL = ƩPIQI/Ʃ PoQo LASPEYRES PRICE INDEX Computed by using quantities of the base period of all other years. ADVANTAGE – Price index for all years can be compared IL = ƩPIQI/Ʃ PoQo PAASCHE PRICE INDEX Computed by using the quantities for the year of interest in computations for a given year. ADVANTAGE – Incorporates current quantity figures in the calculations. IL = ƩPIQI/ƩPoQi