A comparison of conditioned versus unconditioned forecasts of the V AR(l) process

Abstract

The properties of a forecast usually depend upon whether the forecast is conditioned on the final period observation or not. In the case of unconditioned forecasts it is well known that the point predictions are unbiased. If on the other hand the forecast is conditional, then the forecast may be biased. Existing analytical results in literature are insufficient for describing the properties of the conditioned forecast properly, particularly in multivariate models. This paper examines some finite sample properties of conditioned forecasts of the VAR(l) process by means of Monte Carlo experiments. We use a number of parameter settings for the V AR( 1) process to demonstrate that the forecast bias of the conditioned forecast may be considerable. Hence, unless the analyst has a clear idea of whether the conditioned or unconditioned forecast is relevant for the time series being analysed, statistical inferences may be seriously erratic.