Toward optimal multistep forecasts in non-stationary autoregressions

Details Toward optimal multistep forecasts in non-stationary autoregressions Toward optimal multistep forecasts in non-stationary autoregressions

2009-06-12

arxiv.org/abs/0906.2266v1

Bernoulli 2009, Vol. 15, No. 2, 402-437

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/08-BEJ165 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/08-BEJ165

This paper investigates multistep prediction errors for non-stationary autoregressive processes with both model order and true parameters unknown. We give asymptotic expressions for the multistep mean squared prediction errors and accumulated prediction errors of two important methods, plug-in and direct prediction. These expressions not only characterize how the prediction errors are influenced by the model orders, prediction methods, values of parameters and unit roots, but also inspire us to construct some new predictor selection criteria that can ultimately choose the best combination of the model order and prediction method with probability 1. Finally, simulation analysis confirms the satisfactory finite sample performance of the newly proposed criteria.

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