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 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 containing the order p of the autoregressive model that the observation represents
• AIC, a numeric variable containing the value of the information criterion AICp
• SIGFl, numeric variables containing 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 containing 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 containing 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 containing 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 p is given by SIGFl in the kth observation. The k,lth element of p is given by SIGBl in the kth observation.

Table 18.1 shows an example of the OUTAR= data set, with ARMAX=3 and xt of dimension 2. In Table 18.1, (i,j) indicate the i,jth element of the matrix.

Table 18.1: 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 AIC0 0(1,1) 0(1,2) 0(1,1) 0(1,2) . . . . . 2 0 AIC0 0(2,1) 0(2,2) 0(2,1) 0(2,2) . . . . . 3 1 AIC1 1(1,1) 1(1,2) 1(1,1) 1(1,2) (1,1) (1,2) . . . 4 1 AIC1 1(2,1) 1(1,2) 1(2,1) 1(1,2) (2,1) (2,2) . . . 5 2 AIC2 2(1,1) 2(1,2) 2(1,1) 2(1,2) (1,1) (1,2) (1,1) (1,2) . 6 2 AIC2 2(2,1) 2(1,2) 2(2,1) 2(1,2) (2,1) (2,2) (2,1) (2,2) . 7 3 AIC3 3(1,1) 3(1,2) 3(1,1) 3(1,2) (1,1) (1,2) (1,1) (1,2) (1,1) 8 3 AIC3 3(2,1) 3(1,2) 3(2,1) 3(1,2) (2,1) (2,2) (2,1) (2,2) (2,1)

 Obs FOR3_2 BACK1_1 BACK1_2 BACK2_1 BACK2_2 BACK3_1 BACK3_2 1 . . . . . . . 2 . . . . . . . 3 . (1,1) (1,2) . . . . 4 . (2,1) (2,2) . . . . 5 . (1,1) (1,2) (1,1) (1,2) . . 6 . (2,1) (2,2) (2,1) (2,2) . . 7 (1,2) (1,1) (1,2) (1,1) (1,2) (1,1) (1,2) 8 (2,2) (2,1) (2,2) (2,1) (2,2) (2,1) (2,2)

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.

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