low level estimation of a bayesian VAR model
rbvar=bvar1(nlag,tight,weight,decay,y,x)
* nlag = the lag length of the VAR
* tight = Litterman's tightness hyperparameter
* weight = Litterman's weight (matrix or scalar)
* decay = Litterman's lag decay = lag^(-decay)
* y = (nobs x neqs) matrix of endogenous variables
* x = (nobs x nx) matrix of exogenous variables (optional)
* rbvar = a results tlist with:
. rbvar('meth') = 'bvar'
. rbvar('y') = y data vector
. rbvar('x') = x data matrix
. rbvar('nvar') = # exogenous variables
. rbvar('nobs') = # observations
. rbvar('neqs') = # endogenous variables
. rbvar('nlag') = # lags
. rbvar('tight') = Litterman's tightness hyperparameter
. rbvar('weight') = Litterman's weight (matrix or scalar)
. rbvar('decay') = Litterman's lag decay = lag^(-decay)
. rbvar('beta') = bhat, with rbvar('beta')(:,i): coefficients for equation # i
. rbvar('tstat') = t-stats, with rbvar('tstat')(:,i): t-stat for equation # i
. rbvar('pvalue')= pvalue of the betas, with rbvar('pvalue')(:,i): p-value for equation # i
. rbvar('resid') = residuals, with rbvar('resid')(:,i): residuals for equation # i
. rbvar('yhat') = yhat, with rbvar('yhat')(:,i): residuals for equation # i
. rbvar('sige') = estimated variances rbvar('sige')(i): variance for equation # i
. rbvar('ser') = standard errors of the regression with rbvar('ser')(i): standard error for equation # i
. rbvar('dw') = Durbin-Watson Statistic, with: rbvar('dw')(i): DW for equation # i
. rbvar('rsqr') = rsquared, with rbvar('rsqr')(i) : rsquared for equation # i
. rbvar('rbar') = rbar-squared
. rbvar('sigma') = (neqs x neqs) var-covar matrix of the regression
. rbvar('nx') = # exogenous variables
. rbvar('prescte') = boolean indicating the presence or absence of a constant in the regression
. rbvar('xpxi) = inv(x'*x)