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Econometrics Procedures
 

UCM Procedure

Modeling an Autoregression

An autoregression of order one can be thought of as a special case of a cycle when the frequency lamda is either 0 or pi. Modeling this special case separately helps interpretation and parameter estimation. The autoregression component r Subscript t is modeled as

r Subscript t Baseline equals rho r Subscript t minus 1 Baseline plus nu Subscript t Baseline comma nu Subscript t Baseline tilde normal i normal i normal d upper N left parenthesis 0 comma sigma Subscript nu Superscript 2 Baseline right parenthesis

where negative 1 less than or equals rho less than 1. An autoregression can also provide an alternative to the IRREGULAR component when the model errors show some autocorrelation. You can incorporate an autoregression in your model by using the AUTOREG statement.

Last updated: July 09, 2026