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
| Missing Values and Estimation and Forecasting |
Estimation and forecasting are carried out in the presence of missing values by forecasting the missing values with the current set of parameter estimates. The maximum likelihood algorithm employed was suggested by Jones (1980) and is used for both unconditional least squares (ULS) and maximum likelihood (ML) estimation.
The CLS algorithm simply fills in missing values with infinite memory forecast values, computed by forecasting ahead from the nonmissing past values as far as required by the structure of the missing values. These artificial values are then employed in the nonmissing value CLS algorithm. Artificial values are updated at each iteration along with parameter estimates.
For models with input variables, embedded missing values (that is, missing values other than at the beginning or end of the series) are not generally supported. Embedded missing values in input variables are supported for the special case of a multiple regression model that has ARIMA errors. A multiple regression model is specified by an INPUT= option that simply lists the input variables (possibly with lag shifts) without any numerator or denominator transfer function factors. One-step-ahead forecasts are not available for the response variable when one or more of the input variables have missing values.
When embedded missing values are present for a model with complex transfer functions, PROC ARIMA uses the first continuous nonmissing piece of each series to do the analysis. That is, PROC ARIMA skips observations at the beginning of each series until it encounters a nonmissing value and then uses the data from there until it encounters another missing value or until the end of the data is reached. This makes the current version of PROC ARIMA compatible with earlier releases that did not allow embedded missing values.