The ARIMA Procedure
- Overview
-
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
-
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
-
Examples
- References
| Specifying Inputs and Transfer Functions |
Input variables and transfer functions for them can be specified using the INPUT= option in the ESTIMATE statement. The variables used in the INPUT= option must be included in the CROSSCORR= list in the previous IDENTIFY statement. If any differencing is specified in the CROSSCORR= list, then the differenced variable is used as the input to the transfer function.
General Syntax of the INPUT= Option
The general syntax of the INPUT= option is
ESTIMATE ...INPUT=( transfer-function variable ...)
The transfer function for an input variable is optional. The name of a variable by itself can be used to specify a pure regression term for the variable.
If specified, the syntax of the transfer function is
S is the number of periods of time delay (lag) for this input series. Each term in parentheses specifies a polynomial factor with parameters at the lags specified by the 
values. The terms before the slash (/) are numerator factors. The terms after the slash (/) are denominator factors. All three parts are optional.
Commas can optionally be used between input specifications to make the INPUT= option more readable. The $ sign after the shift is also optional.
Except for the first numerator factor, each of the terms 
indicates a factor of the form
 |
The form of the first numerator factor depends on the ALTPARM option. By default, the constant 1 in the first numerator factor is replaced with a free parameter 
.
Alternative Model Parameterization
When the ALTPARM option is specified, the parameter is factored out so that it multiplies the entire transfer function, and the first numerator factor has the same form as the other factors.
The ALTPARM option does not materially affect the results; it just presents the results differently. Some people prefer to see the model written one way, while others prefer the alternative representation. Table 7.9 illustrates the effect of the ALTPARM option.
INPUT= Option |
ALTPARM |
Model |
INPUT=((1 2)(12)/(1)X); |
No |
|
Yes |
|
Differencing and Input Variables
If you difference the response series and use input variables, take care that the differencing operations do not change the meaning of the model. For example, if you want to fit the model
 |
then the IDENTIFY statement must read
identify var=y(1,12) crosscorr=x(1,12); estimate q=1 input=(/(1)x) noconstant;
If instead you specify the differencing as
identify var=y(1,12) crosscorr=x; estimate q=1 input=(/(1)x) noconstant;
then the model being requested is
 |
which is a very different model.
The point to remember is that a differencing operation requested for the response variable specified by the VAR= option is applied only to that variable and not to the noise term of the model.