Sankhya: The Indian Journal of Statistics

1999, Volume 61, Series A, Pt. 2, 241-253

SEQUENTIAL ESTIMATION OF THE AUTOREGRESSIVE PARAMETERS IN GENERAL VECTOR AUTOREGRESSIVE MODEL

By

A.K. BASU,

and

INDRANIL MUKHOPADHYAY, Calcutta University, Calcutta

SUMMARY. This paper considers the problem of sequential point estimation of the autoregressive parameters in a p-th order vector autoregressive model. The sequential estimator proposed here is based on the least square estimator and is shown to be asymptotically risk efficient as the cost of estimation error tends to infinity, under certain regularity conditions. The asymptotic normality and uniform integrability of the standardised stopping time are established. The results generalise the works of Sriram (1988), Martinsek (1990), Basu and Das (1993) and many others.

AMS (1991) subject classification. Primary 62L12, 62M10; secondary 62H12, 90A19.

Key words and phrases. Sequential estimation, non-linear renewal theory, multivariate AR (p) model, asymptotic risk efficiency.

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