The ARIMA Procedure
- Overview
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Getting Started
The Three Stages of ARIMA Modeling Identification Stage Estimation and Diagnostic Checking Stage Forecasting Stage Using ARIMA Procedure Statements General Notation for ARIMA Models Stationarity Differencing Subset, Seasonal, and Factored ARMA Models Input Variables and Regression with ARMA Errors Intervention Models and Interrupted Time Series Rational Transfer Functions and Distributed Lag Models Forecasting with Input Variables Data Requirements -
Syntax
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Details
The Inverse Autocorrelation Function The Partial Autocorrelation Function The Cross-Correlation Function The ESACF Method The MINIC Method The SCAN Method Stationarity Tests Prewhitening Identifying Transfer Function Models Missing Values and Autocorrelations Estimation Details Specifying Inputs and Transfer Functions Initial Values Stationarity and Invertibility Naming of Model Parameters Missing Values and Estimation and Forecasting Forecasting Details Forecasting Log Transformed Data Specifying Series Periodicity Detecting Outliers OUT= Data Set OUTCOV= Data Set OUTEST= Data Set OUTMODEL= SAS Data Set OUTSTAT= Data Set Printed Output ODS Table Names Statistical Graphics
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Examples
- References
| Initial Values |
The syntax for giving initial values to transfer function parameters in the INITVAL= option parallels the syntax of the INPUT= option. For each transfer function in the INPUT= option, the INITVAL= option should give an initialization specification followed by the input series name. The initialization specification for each transfer function has the form
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where C is the lag 0 term in the first numerator factor of the transfer function (or the overall scale factor if the ALTPARM option is specified) and 
is the coefficient of the 
element in the transfer function.
To illustrate, suppose you want to fit the model
 |
and start the estimation process with the initial values 
=10, 
=1, 
=0.5, 
=0.03, 
=0.8, 
=–0.1, 
=0.002, 
=0.1, 
=0.01. (These are arbitrary values for illustration only.) You would use the following statements:
identify var=y crosscorr=x;
estimate p=(1,3) input=(3$(1,2)/(1,2,3)x)
mu=10 ar=.1 .01
initval=(1$(.5,.03)/(.8,-.1,.002)x);
Note that the lags specified for a particular factor are sorted, so initial values should be given in sorted order. For example, if the P= option had been entered as P=(3,1) instead of P=(1,3), the model would be the same and so would the AR= option. Sorting is done within all factors, including transfer function factors, so initial values should always be given in order of increasing lags.
Here is another illustration, showing initialization for a factored model with multiple inputs. The model is
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and the initial values are =10, 
=5, 
=0.8, 
=1, 
=0.5, 
=0.1, 
=0.05, and 
=0.01. You would use the following statements:
identify var=y crosscorr=(w x);
estimate p=(1)(6,12) input=(/(1)w, 3$(1)x)
mu=10 ar=.1 .05 .01
initval=(5$/(.8)w 1$(.5)x);