Bayesian Vector Autoregressive Process

The VARMAX Procedure

Bayesian Vector Autoregressive Process

The Bayesian Vector AutoRegressive (BVAR) model is used to avoid problems of collinearity and over-parameterization that often occur with the use of VAR models. BVAR models do this by imposing priors on the AR parameters.

The following statements fit a BVAR(1) model to the simulated data. You specify the PRIOR= option with the hyper-parameters. The LAMBDA=0.9 and THETA=0.1 are hyper-parameters controlling the prior covariance. Part of the VARMAX procedure output is shown in Figure 4.10.

   proc varmax data=simul1;
      model y1 y2 / p=1 noint 
                    prior=(lambda=0.9 theta=0.1);
   run;

The VARMAX Procedure

Type of Model	BVAR(1)
Estimation Method	Method of Moments Estimation
Prior LAMBDA	0.9
Prior THETA	0.1

Model Parameter Estimates
Equation	Parameter	Estimate	Std Error	T Ratio	Prob>\|T\|	Variable
y1(t)	AR1_1_1	1.05623	0.05050	20.92	0.0001	y1(t-1)
	AR1_1_2	-0.34707	0.04824	-7.19	0.0001	y2(t-1)
y2(t)	AR1_2_1	0.40068	0.04889	8.20	0.0001	y1(t-1)
	AR1_2_2	0.48728	0.05740	8.49	0.0001	y2(t-1)

Covariance Matrix for the Innovation
Variable	y1	y2
y1	1.35807	0.44152
y2	0.44152	1.45070

Figure 4.10: Parameter Estimates for BVAR(1) Model

The output in Figure 4.10 shows that parameter estimates are slightly different from those in Figure 4.3. By choosing the appropriate priors, you may be able to get more accurate forecasts using a BVAR model rather than using an unconstrained VAR model.

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