UCM Procedure

AUTOREG Statement

AUTOREG <options>;

The AUTOREG statement specifies an autoregressive component in the model. An autoregressive component is a special case of cycle that corresponds to the frequency of zero or . It is modeled separately for easier interpretation. A stochastic equation for an autoregressive component can be written as follows:

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

The damping factor can take any value in the interval (–1, 1), including –1 but excluding 1. If , the autoregressive component cannot be distinguished from the random walk level component. If , the autoregressive component corresponds to a seasonal component with a season length of 2, or a nonstationary cycle with period 2. If , then the autoregressive component is stationary. The following example illustrates the AUTOREG statement. This statement includes an autoregressive component in the model. The damping factor and the disturbance variance are estimated from the data.

   autoreg;

NOEST=RHO NOEST=VARIANCE NOEST=(RHO VARIANCE): fixes the values of and to those specified in the RHO= and VARIANCE= options.
PLOT=FILTER PLOT=SMOOTH PLOT=( <FILTER> <SMOOTH> ): requests plotting of the filtered or smoothed estimate of the autoreg component.
PRINT=FILTER PRINT=SMOOTH PRINT=(<FILTER> <SMOOTH>): requests printing of the filtered or smoothed estimate of the autoreg component.
RHO=value: specifies an initial value for the damping factor during the parameter estimation process. The value of must be in the interval (–1, 1), including –1 but excluding 1.
VARIANCE=value: specifies an initial value for the disturbance variance during the parameter estimation process. Any nonnegative value, including zero, is an acceptable starting value.

Last updated: June 19, 2025