Ecm time series forecast

ECONOMETRICS PROJECT PRESENTATION
Time Series Analysis in SAS
AYAPPARAJ SKS | ADITYA NATHIREDDY | VIBEESH CS |
NEHA NEHRA

AGENDA
 TIME SERIES FORECASTING – INTRODUCTION
 THINGS TO BE CHECKED BEFORE APPLYING TIME
SERIES MODELLING
 BUSINESS OBJECTIVE
 ABOUT THE DATASET
 DATA PREPARATION
 MODEL IDENTIFICATION AND ESTIMATION
 GENERATING FORECAST
 FINAL FORECAST

TIME SERIES FORECASTING - INTRODUCTION
 Time Series relates to values taken by a variable over time (such as daily
sales revenue, weekly orders, monthly overheads, yearly income) and
tabulated or plotted as chronologically ordered numbers or data points to
yield valid statistical inferences.

 VOLATILITY :
 Data should not be very volatile for time series method.
 For stable changes, it is a good method.
 HOW IT CAN BE CHECKED :
 Scatter plot of the data with time in the horizontal axis and the time series
in the vertical axis gives indications for this.
 Fan or Inverted Fan distribution of the scatter plot shows the data is highly
volatile.
 WHAT CAN BE DONE TO OVERCOME THE PROBLEM :
 Transformations has to be done for the data based on the distribution of
the plot
 For Fan shape distribution - decrease the scale of the data – log / Sqrt
 While for Inverted Fan distribution - increase the scale of the data –
exponential / square .
THINGS TO BE CHECKED BEFORE
APPLYING TIME SERIES MODELLING

 PATTERN :
 If the past has a pattern, then time series will yield good result.
 Absence of pattern will have no effect of this method on the data.
 For stable changes, it is a good method.
 STATIONARITY OF THE DATA :
 If the data is stationary, there will not be any problem in using the
technique.
 if a data is a complete random memory less process with no fixed pattern
it is called non stationary data and cannot be used for future forecasting
this is checked using “Augmented Dickey Fuller unit root (ADF) test“.
 HOW DO WE PERFORM ADF TEST :
 We perform Hypothesis to determine the whether the data is stationary or
not.
 Ho : Non stationary /// Ha : Stationary
 if p < alpha we reject the Ho to claim that the data is stationary and
hence it cant be used for forecasting.
 if p > alpha we accept the Ho to claim that the data is non stationary
which can be made stationary by differencing.

BUSINESS OBJECTIVE
[To project the airline travel for the next 12 months]

 Sashelp.air — Airline Data (Monthly: Jan49-Dec60)
• The dataset used here is SASHELP.AIR which is
Airline data and contains two variables – DATE and
AIR (labelled as International Airline Travel). It
contains the data from JAN 1949 to DEC 1960.
ABOUT THE DATASET

 CHECK FOR VOLATILITY :
• Plot between the two variables yielded a
distribution as shown below.
• So we are going for variable transformation.
DATA PREPARATION

 CHECK FOR VOLATILITY :
• We are doing both log and sqrt transformations.
• From the below plots it is visible that log
transformation yields a good plot.

 CHECK FOR STATIONARY CONDITION OF DATA (PROC ARIMA OUTPUT)
• Now the result shows there is no stationarity
based on p values(all p values should be less than
alpha 0.01% or 0.0001) so we have to do
differencing.
• Now all the p values are less than alpha.

 CHECK FOR SEASONALITY :
• Auto correlation (ACF) captures correlation btw Yt
and Yt-s where S is the period of lag if the ACF
exhibits high a value at fixed interval then that
interval is considered as the period of
seasonality.
• Differencing of the same order will de seasonalize
the data.
• The output of ACF shows the period of seasonality
is 12 years.
 DESESONALIZATION :
• We are desesonalizing the data by 12th order
differencing as it gives high correlation values.

 CREATION OF DEVELOPMENT AND VALIDATION OF DATA :
• Depending upon number of observations, some of the
most recent time point data are put aside as the
validation sample.
• The rest of the data, development sample, is used
to generate forecast for multiple models which are
compared with the actuals stored in the
development sample.
MODEL IDENTIFICATION AND
ESTIMATION

 SELECTION OF P(AUTO REGRESSIVE)AND Q (MOVING AVERAGE) :
• The model selection criteria namely AIC BIC SBC
(Lower the values it is better)are used to select
the values of P and Q.
• AIC - Akaike's information criteria
• BIC - Bayesian information criteria
• SBC - Schwartz bayesian criteria
• BIC :: p 0-5 q 0-5
• The minic (minimum information criteria) under
proc arima generates the minimum BIC model after
considering all combinations of P and Q from 0 to
5.
• This selects all models in the neighbourhood of
the minimum BIC models, generate AIC SBC and
calculate average of AIC and SBC.
• Then select 6 to 7 models based on relative lower
value of average and generate forecasts for them.

 Contd..,
• By observation, we can see that the minimum of the
matrix is -6.3503 corresponding to AR3 and MA0
location (P,Q)=>(3,0).
• This selects all models in the neighbourhood of
the minimum BIC models, generate AIC SBC and
calculate average of AIC and SBC.
• Then select 6 to 7 models based on relative lower
value of average and generate forecasts for them.

• For each combinations of p and q selected from AIC
and SBC, generate forecast using the forecast
under proc arima where,
 lead = Number of future time points to forecast
 ID = Name of the time variable
 Interval = Unit of the time variable
 Out = Output file which saves the forecast.
• The forecasts obtained for each combination for p
and q is compared with the actuals of the same
time points stored in the validation file using
MAPE(Mean Absolute Percentage Error).
• The combination with the minimum MAPE is selected.
GENERATING FORECAST

• The combination with the minimum MAPE is selected
and the same is applied to the entire data to
generate the final forecast.
• Ran forecast on the full data for the best p and q
combination.
FINAL FORECAST

Ecm time series forecast

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