Toward optimal multistep forecasts in non-stationary autoregressions

TL;DR

This paper derives asymptotic expressions for multistep prediction errors in non-stationary autoregressive models, proposing new criteria for optimal predictor selection that outperform existing methods.

Contribution

It provides novel asymptotic formulas for prediction errors and introduces new predictor selection criteria for non-stationary autoregressive processes.

Findings

Asymptotic expressions characterize prediction errors influenced by model parameters.

New criteria effectively select optimal model order and prediction method.

Simulation confirms the criteria's strong finite sample performance.

Abstract

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.