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
Stationarity Tests
When a time series has a unit root, the series is nonstationary and the ordinary least squares (OLS) estimator is not normally distributed. Dickey and Fuller studied the limiting distribution of the OLS estimator of autoregressive models for time series with a simple unit root (Dickey 1976; Dickey and Fuller 1979). Dickey, Hasza, and Fuller obtained the limiting distribution for time series with seasonal unit roots (Dickey, Hasza, and Fuller 1984). Hamilton (1994) discusses the various types of unit root testing.
For a description of Dickey-Fuller tests, see the section PROBDF Function for Dickey-Fuller Tests in Chapter 6. See Chapter 9: The AUTOREG Procedure, for a description of Phillips-Perron tests.
The random-walk-with-drift test recommends whether or not an integrated times series has a drift term. Hamilton (1994) discusses this test.