The ARIMA Procedure
- Overview
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Getting Started
The Three Stages of ARIMA ModelingIdentification StageEstimation and Diagnostic Checking StageForecasting StageUsing ARIMA Procedure StatementsGeneral Notation for ARIMA ModelsStationarityDifferencingSubset, Seasonal, and Factored ARMA ModelsInput Variables and Regression with ARMA ErrorsIntervention Models and Interrupted Time SeriesRational Transfer Functions and Distributed Lag ModelsForecasting with Input VariablesData Requirements -
Syntax
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DetailsThe Inverse Autocorrelation FunctionThe Partial Autocorrelation FunctionThe Cross-Correlation FunctionThe ESACF MethodThe MINIC MethodThe SCAN MethodStationarity TestsPrewhiteningIdentifying Transfer Function ModelsMissing Values and AutocorrelationsEstimation DetailsSpecifying Inputs and Transfer FunctionsInitial ValuesStationarity and InvertibilityNaming of Model ParametersMissing Values and Estimation and ForecastingForecasting DetailsForecasting Log Transformed DataSpecifying Series PeriodicityDetecting OutliersOUT= Data SetOUTCOV= Data SetOUTEST= Data SetOUTMODEL= SAS Data SetOUTSTAT= Data SetPrinted OutputODS Table NamesStatistical Graphics
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Examples
- References
In the table of parameter estimates produced by the ESTIMATE statement, model parameters are referred to by using the naming convention described in this section.
The parameters in the noise part of the model are named as ARi,j or MAi,j, where AR refers to autoregressive parameters and MA to moving-average parameters. The subscript i refers to the particular polynomial factor, and the subscript j refers to the jth term within the ith factor. These terms are sorted in order of increasing lag within factors, so the subscript j refers to the jth term after sorting.
When inputs are used in the model, the parameters of each transfer function are named NUMi,j and DENi,j. The jth term in the ith factor of a numerator polynomial is named NUMi,j. The jth term in the ith factor of a denominator polynomial is named DENi,j.
This naming process is repeated for each input variable, so if there are multiple inputs, parameters in transfer functions for different input series have the same name. The table of parameter estimates shows in the “Variable” column the input with which each parameter is associated. The parameter name shown in the “Parameter” column and the input variable name shown in the “Variable” column must be combined to fully identify transfer function parameters.
The lag 0 parameter in the first numerator factor for the first input variable is named NUM1. For subsequent input variables, the lag 0 parameter in the first numerator factor is named NUMk, where k is the position of the input variable in the INPUT= option list. If the ALTPARM option is specified, the NUMk parameter is replaced by an overall scale parameter named SCALEk.
For the mean and noise process parameters, the response series name is shown in the “Variable” column. The lag and shift for each parameter are also shown in the table of parameter estimates when inputs are used.