First-order random coefficient autoregressive (RCA(1)) model: Joint whittle estimation and information

Abstract

Random coefficient autoregressive model, RCA(p), has been discussed widely as a suitable model for nonlinear time series. The con- ditional least squares and likelihood parameter estimation of RCA(p) model has also been discussed in [3]. The statistical inference of RCA(1) model has been presented in [4] while the conditional least square es- timates for nonstationary processes is studied in [7]. The optimal es- timation for nonlinear time series using estimating equations has been investigated in [6]. Recently there has been interest in joint prediction based on spectral density of popular nonlinear time series models such as RCA(p) models. Another way of estimating the parameters of the RCA(1) model is to do Whittle's estimation. In this paper the Whittle estimates of the parameters of an RCA(p) model are studied. It is shown that the Whittle information of the autoregressive parameter in an RCA(p) model is larger than the corresponding information in an autoregressive (AR) model. Key words and phrases. Non-linear time series, RCA model, Whittle's estimation and information.