PROC UCM: AUTOREG Statement :: SAS/ETS(R) 9.22 User's Guide

The 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 $\text{[math]}$ . It is modeled separately for easier interpretation. A stochastic equation for an autoregressive component $\text{[math]}$ can be written as follows:

$\text{[math]}$

The damping factor $\text{[math]}$ can take any value in the interval (–1, 1), including –1 but excluding 1. If $\text{[math]}$ , the autoregressive component cannot be distinguished from the random walk level component. If $\text{[math]}$ , the autoregressive component corresponds to a seasonal component with a season length of 2, or a nonstationary cycle with period 2. If $\text{[math]}$ , 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 $\text{[math]}$ and the disturbance variance $\text{[math]}$ are estimated from the data.

      autoreg;

NOEST=RHO
NOEST=VARIANCE
NOEST=(RHO VARIANCE): fixes the values of $\text{[math]}$ and $\text{[math]}$ 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 $\text{[math]}$ during the parameter estimation process. The value of $\text{[math]}$ must be in the interval (–1, 1), including –1 but excluding 1.
VARIANCE=value: specifies an initial value for the disturbance variance $\text{[math]}$ during the parameter estimation process. Any nonnegative value, including zero, is an acceptable starting value.

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