Prediction from the Dynamic Simultaneous Equation Model with Vector Autoregressive Errors

IN THIS PAPER we derive the asymptotic distribution of multistep prediction from the general dynamic simultaneous equation model. The approach taken is a generalization of that of Schmidt [4] who considered a model with uncorrelated errors. It seems worthwhile to extend Schmidt's results, since the estimation of dynamic simultaneous equation models with autoregressive errors is now fairly commonplace in the literature. Also, as noted by Schmidt [5], the effects of parameter estimation can produce a significant effect on forecast confidence intervals. In fact, the results we obtain are computationally feasible making it possible to calculate the term due to parameter estimation in a forecast confidence interval. For the seemingly unrelated regression model with vector autoregressive errors, but with no lagged dependent variables, the results turn out to be particularly straightforward generalizations of those obtained by Baillie [1], who considered the single equation regression model with autoregressive errors.