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 36.17.
/*--- 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 36.17 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 36.17: Parameter Estimates for the BVECM(2) Form
Type of Model | BVECM(2) |
---|---|
Estimation Method | Maximum Likelihood Estimation |
Cointegrated Rank | 1 |
Prior Lambda | 0.5 |
Prior Theta | 0.2 |
Alpha | |
---|---|
Variable | 1 |
y1 | -0.34392 |
y2 | 0.16659 |
Parameter Alpha * Beta' Estimates | ||
---|---|---|
Variable | y1 | y2 |
y1 | -0.34392 | 0.67262 |
y2 | 0.16659 | -0.32581 |
AR Coefficients of Differenced Lag | |||
---|---|---|---|
DIF Lag | Variable | y1 | y2 |
1 | y1 | -0.80070 | -0.59320 |
y2 | 0.33417 | -0.53480 |