Estimation and Forecasting in First-order Vector Autoregressions with Near to Unit Roots and Conditional

This paper investigates the effects of imposing invalid cointegration restrictions or ignoring valid ones on the estimation, testing and forecasting properties of the bivariate, first-order, vector autoregressive (VAR(1)) model. We first consider nearly cointegrated VARs, that is stable systems whose largest root, λmax, lies in the neighborhood of unity, while the other root, λmin, is safely smaller than unity. In this context, we define the ‘forecast cost of type I ’ to be the deterioration in the forecasting accuracy of the VAR model due to the imposition of invalid cointegration restrictions. However, there are cases where misspecification arises for the opposite reasons, namely from ignoring cointegration when the true process is, in fact, cointegrated. Such cases can arise when λmax equals unity and λmin is less than but near to unity. The effects of this type of misspecification on forecasting will be referred to as ‘forecast cost of type II’. By means of Monte Carlo simulations, we measure both types of forecast cost in actual situations, where the researcher is led (or misled) by the usual unit root tests in choosing the unit root structure of the system. We consider VAR(1) processes driven by iid Gaussian or GARCH innovations. To distinguish between the effects of non-linear dependence and those of leptokurtosis, we also consider processes driven by iid t(2) innovations. The simulation results reveal that the forecast cost of imposing invalid cointegration restriction