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Bayesian Vector Error Correction Model
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Bayesian inference on a cointegrated system begins by using the priors of
obtained from the VECM(
) form. Bayesian vector error correction models can improve forecast accuracy for cointegrated processes.
The following statements fit a BVECM(2) form to the simulated data. You specify both the PRIOR= and ECM= options for the Bayesian vector error correction model. The VARMAX procedure output is shown in Figure 35.17.
/*--- Bayesian Vector Error-Correction Model ---*/
proc varmax data=simul2;
model y1 y2 / p=2 noint
prior=( lambda=0.5 theta=0.2 )
ecm=( rank=1 normalize=y1 )
print=(estimates);
run;
Figure 35.17 shows the model type fitted to the data, the estimates of the adjustment coefficient (
), the parameter estimates in terms of lag one coefficients (
), and lag one first differenced coefficients (
).
Figure 35.17
Parameter Estimates for the BVECM(2) Form
The VARMAX Procedure
BVECM(2) |
Maximum Likelihood Estimation |
1 |
0.5 |
0.2 |
-0.34392 |
0.67262 |
0.16659 |
-0.32581 |
-0.80070 |
-0.59320 |
0.33417 |
-0.53480 |
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