On Optimal Adaptive Prediction of Multivariate Autoregression

Abstract

The problem of asymptotic efficiency of adaptive one-step predictors for a stable multivariate first-order autoregressive process (AR(1)) with unknown parameters is considered. The predictors are based on the truncated estimators of the dynamic matrix parameter. The truncated estimation method is a modification of the truncated sequential estimation method that makes it possible to obtain estimators of ratio-type functionals with a given accuracy by samples of fixed size. The criterion of optimality is based on the loss function, defined as a sum of sample size and squared prediction error's sample mean. The cases of known and unknown variance of the noise model are studied. In the latter case the optimal sample size is a special stopping time. The simulation results are given.

Keywords:

• Adaptive predictors
• Asymptotic risk efficiency
• Multivariate autoregression
• Optimal sample size
• Stopping time
• Truncated parameter estimators

Subject Classifications:

• 60G25
• 60G40
• 62F35
• 62H12
• 62J05
• 62L10

ACKNOWLEDGMENTS

The authors thank the Associate Editor as well as the Editor-in-Chief, Professor Nitis Mukhopadhyay, for their careful reading and valuable comments, which helped to improve this article.

Notes

Recommended by R. W. Keener