# The STATESPACE Procedure

### OUTAR= Data Set

The OUTAR= data set contains the estimates of the preliminary autoregressive models. The OUTAR= data set contains the following variables:

• ORDER, a numeric variable that contains the order p of the autoregressive model that the observation represents

• AIC, a numeric variable that contains the value of the information criterion

• SIGFl, numeric variables that contain the estimate of the innovation covariance matrices for the forward autoregressive models. The variable SIGFl contains the lth column of in the observations with ORDER=p.

• SIGBl, numeric variables that contain the estimate of the innovation covariance matrices for the backward autoregressive models. The variable SIGBl contains the lth column of in the observations with ORDER=p.

• FORk _l, numeric variables that contain the estimates of the autoregressive parameter matrices for the forward models. The variable FORk _l contains the lth column of the lag k autoregressive parameter matrix in the observations with ORDER=p.

• BACk _l, numeric variables that contain the estimates of the autoregressive parameter matrices for the backward models. The variable BACk _l contains the lth column of the lag k autoregressive parameter matrix in the observations with ORDER=p.

The estimates for the order p autoregressive model can be selected as those observations with ORDER=p. Within these observations, the k,lth element of is given by the value of the FORi _l variable in the kth observation. The k,lth element of is given by the value of BACi _l variable in the kth observation. The k,lth element of is given by SIGFl in the kth observation. The k,lth element of is given by SIGBl in the kth observation.

Table 28.2 shows an example of the OUTAR= data set, with ARMAX=3 and of dimension 2. In Table 28.2, indicate the i,jth element of the matrix.

Table 28.2: Values in the OUTAR= Data Set

 Obs ORDER AIC SIGF1 SIGF2 SIGB1 SIGB2 FOR1_1 FOR1_2 FOR2_1 FOR2_2 FOR3_1 1 0 AIC . . . . . 2 0 AIC . . . . . 3 1 AIC . . . 4 1 AIC . . . 5 2 AIC . 6 2 AIC . 7 3 AIC 8 3 AIC

Obs

FOR3_2

BACK1_1

BACK1_2

BACK2_1

BACK2_2

BACK3_1

BACK3_2

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2

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3

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4

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5

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6

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7

8

The estimated autoregressive parameters can be used in the IML procedure to obtain autoregressive estimates of the spectral density function or forecasts based on the autoregressive models.