Loss Function vs. Likelihood Estimation of Forecasting Models: A Pre-test Procedure and a Bayesian Interpretation

The paper considers the problem of using a vector autoregression (VAR) to forecast a stationary process several periods into the future. If the V AR is misspecified, it might be best to use the loss function under which the forecasts are evaluated also for parameter estimation. It is a plausible and straightforward procedure to conduct a model check of the V AR before adopting a loss function estimator. If the V AR is discredited by the data then a loss function estimator is used, otherwise the parameters are estimated by a likelihood based technique. We calculate the asymptotic prediction risk for such a pre-test procedure under the assumptions that the data are generated from a linear process that drifts toward the VAR as the sample size tends to infinity. The pre-test can avoid picking the inferior estimator when the stakes are high. This is confirmed by a small Monte Carlo study. A Bayesian interpretation of loss function estimation and the pre-test procedure is provided. A forecaster places non-zero prior probability on a reference model but finds it too onerous to calculate its posterior predictive distribution. Instead he chooses a prediction procedure based on the VAR that has a small integrated prediction risk.

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Paper Number
99-006
Year
1999
Authored by