Risk efficient estimation of fully dependent random coefficient autoregressive models of general order

ABSTRACT

We consider a stochastic dynamic model with autoregressive progression. The drift coefficients of the autoregressive model are random where the randomness in the coefficients can have any dependence structure. We propose a two-step sequential estimator and study the asymptotic behavior of few important properties. Paradigm of sequential estimation has its own advantage in reducing sample size and plugging estimates of nuisance parameters while inferring about the main parameters. Our proposed estimator is asymptotically optimal as the predictive risk of the proposed estimator attains the risk of the oracle that assumes known nuisance parameters. Extensive simulation confirms our results.

KEYWORDS:

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

MATHEMATICS SUBJECT CLASSIFICATION:

• 62M10
• 62L12

Acknowledgment

The corresponding author respectfully acknowledges that the idea of this problem emerged with his discussion with Late Professor Adhir Kumar Basu of University of Calcutta.