OUTAR= Data Set :: SAS/ETS(R) 13.1 User's Guide

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 ${AIC_{p}}$
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 ${\widehat{\bSigma }_{p}}$ 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 ${\widehat{\bOmega }_{p}}$ 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 ${ \widehat{\bPhi }^{p}_{k}}$ 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 ${ \widehat{\bPsi }^{p}_{k}}$ 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 ${ \bPhi ^{p}_{i}}$ is given by the value of the FORi _l variable in the kth observation. The k,lth element of ${ \bPsi ^{p}_{i}}$ is given by the value of BACi _l variable in the kth observation. The k,lth element of $\bSigma$ $_{\mi {p} }$ is given by SIGFl in the kth observation. The k,lth element of $\bOmega$ $_{\mi {p}}$ is given by SIGBl in the kth observation.

Table 28.2 shows an example of the OUTAR= data set, with ARMAX=3 and ${\mb {x}_{t}}$ of dimension 2. In Table 28.2, ${(i,j)}$ 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 $_{0}$	$\bSigma$ $_{0(1,1)}$	$\bSigma$ $_{0(1,2)}$	$\bOmega$ $_{0(1,1)}$	$\bOmega$ $_{0(1,2)}$	.	.	.	.	.
2	0	AIC $_{0}$	$\bSigma$ $_{0(2,1)}$	$\bSigma$ $_{0(2,2)}$	$\bOmega$ $_{0(2,1)}$	$\bOmega$ $_{0(2,2)}$	.	.	.	.	.
3	1	AIC $_{1}$	$\bSigma$ $_{1(1,1)}$	$\bSigma$ $_{1(1,2)}$	$\bOmega$ $_{1(1,1)}$	$\bOmega$ $_{1(1,2)}$	$\bPhi ^{1}_{1}$ $_{(1,1)}$	$\bPhi ^{1}_{1}$ $_{(1,2)}$	.	.	.
4	1	AIC $_{1}$	$\bSigma$ $_{1(2,1)}$	$\bSigma$ $_{1(1,2)}$	$\bOmega$ $_{1(2,1)}$	$\bOmega$ $_{1(1,2)}$	$\bPhi ^{1}_{1}$ $_{(2,1)}$	$\bPhi ^{1}_{1}$ $_{(2,2)}$	.	.	.
5	2	AIC $_{2}$	$\bSigma$ $_{2(1,1)}$	$\bSigma$ $_{2(1,2)}$	$\bOmega$ $_{2(1,1)}$	$\bOmega$ $_{2(1,2)}$	$\bPhi ^{2}_{1}$ $_{(1,1)}$	$\bPhi ^{2}_{1}$ $_{(1,2)}$	$\bPhi ^{2}_{2}$ $_{(1,1)}$	$\bPhi ^{2}_{2}$ $_{(1,2)}$	.
6	2	AIC $_{2}$	$\bSigma$ $_{2(2,1)}$	$\bSigma$ $_{2(1,2)}$	$\bOmega$ $_{2(2,1)}$	$\bOmega$ $_{2(1,2)}$	$\bPhi ^{2}_{1}$ $_{(2,1)}$	$\bPhi ^{2}_{1}$ $_{(2,2)}$	$\bPhi ^{2}_{2}$ $_{(2,1)}$	$\bPhi ^{2}_{2}$ $_{(2,2)}$	.
7	3	AIC $_{3}$	$\bSigma$ $_{3(1,1)}$	$\bSigma$ $_{3(1,2)}$	$\bOmega$ $_{3(1,1)}$	$\bOmega$ $_{3(1,2)}$	$\bPhi ^{3}_{1}$ $_{(1,1)}$	$\bPhi ^{3}_{1}$ $_{(1,2)}$	$\bPhi ^{3}_{2}$ $_{(1,1)}$	$\bPhi ^{3}_{2}$ $_{(1,2)}$	$\bPhi ^{3}_{3}$ $_{(1,1)}$
8	3	AIC $_{3}$	$\bSigma$ $_{3(2,1)}$	$\bSigma$ $_{3(1,2)}$	$\bOmega$ $_{3(2,1)}$	$\bOmega$ $_{3(1,2)}$	$\bPhi ^{3}_{1}$ $_{(2,1)}$	$\bPhi ^{3}_{1}$ $_{(2,2)}$	$\bPhi ^{3}_{2}$ $_{(2,1)}$	$\bPhi ^{3}_{2}$ $_{(2,2)}$	$\bPhi ^{3}_{3}$ $_{(2,1)}$

Obs	FOR3_2	BACK1_1	BACK1_2	BACK2_1	BACK2_2	BACK3_1	BACK3_2
1	.	.	.	.	.	.	.
2	.	.	.	.	.	.	.
3	.	$\bPsi ^{1}_{1}$ $_{(1,1)}$	$\bPsi ^{1}_{1}$ $_{(1,2)}$	.	.	.	.
4	.	$\bPsi ^{1}_{1}$ $_{(2,1)}$	$\bPsi ^{1}_{1}$ $_{(2,2)}$	.	.	.	.
5	.	$\bPsi ^{2}_{1}$ $_{(1,1)}$	$\bPsi ^{2}_{1}$ $_{(1,2)}$	$\bPsi ^{2}_{2}$ $_{(1,1)}$	$\bPsi ^{2}_{2}$ $_{(1,2)}$	.	.
6	.	$\bPsi ^{2}_{1}$ $_{(2,1)}$	$\bPsi ^{2}_{1}$ $_{(2,2)}$	$\bPsi ^{2}_{2}$ $_{(2,1)}$	$\bPsi ^{2}_{2}$ $_{(2,2)}$	.	.
7	$\bPhi ^{3}_{3}$ $_{(1,2)}$	$\bPsi ^{3}_{1}$ $_{(1,1)}$	$\bPsi ^{3}_{1}$ $_{(1,2)}$	$\bPsi ^{3}_{2}$ $_{(1,1)}$	$\bPsi ^{3}_{2}$ $_{(1,2)}$	$\bPsi ^{3}_{3}$ $_{(1,1)}$	$\bPsi ^{3}_{3}$ $_{(1,2)}$
8	$\bPhi ^{3}_{3}$ $_{(2,2)}$	$\bPsi ^{3}_{1}$ $_{(2,1)}$	$\bPsi ^{3}_{1}$ $_{(2,2)}$	$\bPsi ^{3}_{2}$ $_{(2,1)}$	$\bPsi ^{3}_{2}$ $_{(2,2)}$	$\bPsi ^{3}_{3}$ $_{(2,1)}$	$\bPsi ^{3}_{3}$ $_{(2,2)}$

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.

The STATESPACE Procedure

OUTAR= Data Set