Risk-efficient sequential estimation of multivariate random coefficient autoregressive process. Issue 1 (2nd January 2019) - Karmakar, Bikram; Mukhopadhyay, Indranil
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.