BVAR (litterman prior)

[Roman]

Hi Guys,

In the BVAR doc for the litterman prior, it is mentioned that EViews offers three choices of an estimator of the Matrix SIGMA.
One of them is the Univariate AR where SIGMA is a diagonal matrix where the (i,i)-th element is given by the standard OLS estimate of the error variance calculated from an univariate AR regression using the i-th variable.

I have questions regarding the computation of this (i,i)-th SIGMA element:
- What is the order of the AR process used in the computation ?
- Isn't it the same as estimating the BVAR with lamda1, lambda2 and lambda3 all equal to 0 ?
- Is there a way to get this sigma element through a BVAR command ?


Many thanks,

Roman

[Roman]

Hi Guys,

Need help about this, could you please detail the univariate case used for initial residual covariance ?
Is it a simple AR(p) on each endogenous variable (p being endogenous lags)?

Thanks

Roman

[EViews Esther]

EViews specifies the Litterman hyperparameters to be lambda1>0, lambda2 in [0,1] and lambda3>0.
sigma_i and sigma_j are calculated by your choice of the initial covariance options: univariate AR, diagonal VAR, or full VAR estimates.
According to your hyperparameters specification, EViews sets the covariance matrix of residuals (i.e. SIGMA) to be diagonal.

The hyperparameter lambda1 controls the tightness of own and foreign lags. If you set lambda1=0, the posterior equals the prior and the data do not influence the estimates. For lambda1=infinity, the posterior expectations coincide with the OLS estimates. You will get the standard OLS estimates with the BVAR command BVAR(INITCOV=DIAG,L1=inf) 1 #lags var_list.

[EViews Esther]

Need help about this, could you please detail the univariate case used for initial residual covariance ?
Is it a simple AR(p) on each endogenous variable (p being endogenous lags)?

Yes, sigma_i^2s are the variances of residuals from univariate pth order autoregressions.