A Comparison of Conditioned Versus Unconditioned Forecasts of the VAR(1) Process

ABSTRACT

The properties of a forecast usually depend upon whether or not the forecast is conditioned on the final period observation. 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 article examines some finite sample properties of conditioned forecasts of the VAR(1) process by means of Monte Carlo experiments. We use a number of parameter settings for the VAR(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 analyzed, statistical inferences may be seriously erratic.

Key Words:

• Conditioning
• Forecast bias
• Monte Carlo
• VAR(1) process

Mathematics Subject Classification:

• 62M20
• 62A01

Notes

*The TMSEP for the h-step forecast, i.e., trace{ _y (h)}/K, may be calculated by trace{ _y (1)}/K = trace{ _u }/K and trace{ _y (2)}/K = trace{ _u  + A _u A’}/K, (Lutkepohl, 1993).