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
| Stationarity |
The noise (or residual) series for an ARMA model must be stationary, which means that both the expected values of the series and its autocovariance function are independent of time.
The standard way to check for nonstationarity is to plot the series and its autocorrelation function. You can visually examine a graph of the series over time to see if it has a visible trend or if its variability changes noticeably over time. If the series is nonstationary, its autocorrelation function will usually decay slowly.
Another way of checking for stationarity is to use the stationarity tests described in the section Stationarity Tests.
Most time series are nonstationary and must be transformed to a stationary series before the ARIMA modeling process can proceed. If the series has a nonstationary variance, taking the log of the series can help. You can compute the log values in a DATA step and then analyze the log values with PROC ARIMA.
If the series has a trend over time, seasonality, or some other nonstationary pattern, the usual solution is to take the difference of the series from one period to the next and then analyze this differenced series. Sometimes a series might need to be differenced more than once or differenced at lags greater than one period. (If the trend or seasonal effects are very regular, the introduction of explanatory variables can be an appropriate alternative to differencing.)