Risk-efficient sequential estimation of multivariate random coefficient autoregressive process

Abstract

A vector-valued autoregressive time series model is considered. The autoregressive coefficients of the model are random with possible dependencies among them. Estimation of the large number of parameters in such models becomes costly with an increase in dimension. A sequential procedure is proposed that promises a significant gain in the sample size thus reduction in the cost of implementation. The procedure is also risk efficient in the sense that as the cost of sampling becomes negligible the asymptotic predictive risk of the proposed procedure reaches the oracle predictive risk corresponding to the best fixed sample size procedure that assumes the values of the nuisance parameters to be known. Extensive simulation results are presented to illustrate the properties of the proposed procedure in a finite sample.

KEYWORDS:

• Asymptotic risk efficiency
• oracle estimation
• random coefficient vector autoregressive model
• sequential procedure
• time series model

SUBJECT CLASSIFICATIONS:

• 62L10
• 62M10
• 62H12
• 62L12

ACKNOWLEDGMENTS

The authors respectfully acknowledge that the idea of this problem emerged from a discussion with Late Professor Adhir Kumar Basu of University of Calcutta. We are also thankful to the Associate Editor and the referee(s), who spent their valuable time reading our article and recommending improvements.