The Estimation of Random Coefficient Autoregressive Models. I

Abstract

This paper is concerned with autoregressive models in which the coefficients are assumed to be not constant but subject to random perturbations so that we are considering a class of random coefficient autoregressive models. By means of a two stage regression procedure estimates of the unknown parameters of these models are obtained. The estimates are shown to be strongly consistent and to satisfy a central limit theorem. A number of Monte Carlo experiments was carried out to illustrate the estimation procedure and their results are reported.

AR(1) Sequence with Random Coefficients:Regenerative Properties and its Application

“…, X n−1 ) = E(ρ n )X n−1 . For this reason the sequence {X n } satisfying (1.1) is often referred to in the time series literature as Random Coefficient Auto Regressive sequence of order one (RCAR(1)) (see [1,6,7,9]). [5] studied a parametric model for (ρ 1 , ϵ 1 ) under the assumption that ρ 1 and ϵ 1 are independent and provided a consistent estimator of the model parameters.…”

An Investment Strategy Based on Stochastic Unit Root Models

“…There are many methods proposed in the literature to estimate its parameters for trading or forecast purpose. For example Nicholls and Quinn (1981) employed the traditional least squares and the maximum likelihood methods, see also Granger and Swanson (1997). Wang and Ghosh (2002) use Bayesian approach while Sollis et al (2000) work with Kalman filter.…”

On parameter estimation of partly observed bilinear discrete-time stochastic systems

“…A number of papers, including articles, concerning control and filtration problems, deal with parameter estimation problem of such systems (Anderson et al 1969;Box and Jenkins 1970;Brockwell and Davis 1991;Feigin and Tweedie 1985;Fujita and Fukao 1972;Kashkovsky and Konev 2008;Vasiliev 2007, 2008;Murthy and McGriffin 1980;Meyn and Tweedie 1993;Nicholls and Quinn 1980;Pergamenchtchikov and Klüppelberg 2004;Pergamenshchikov and Shiryaev 1992;Rao 1966;Tugnait 1981Tugnait , 1983Konev 1985, 1987a) and there are different approaches to this problem, e.g., linear least squares method, method of stochastic approximation, maximum-likelihood method, correlation methods and others. Moreover, algorithms of linear and nonlinear filtration are used.…”

“…Stability and ergodicity conditions of fully observed multivariate models with drifting parameters were obtained in, e.g., Feigin and Tweedie (1985), Meyn and Tweedie (1993), Nicholls and Quinn (1980).…”

“…The estimation problem of the mean of drifting parameters of the stable autoregressive process was considered, e.g., in Feigin and Tweedie (1985), Kashkovsky and Konev (2008), Malyarenko and Vasiliev (2008), Meyn and Tweedie (1993), Nicholls and Quinn (1980), Pergamenshchikov and Shiryaev (1992). In particular, one-step sequential estimation procedure was obtained in Kashkovsky and Konev (2008), Pergamenshchikov and Shiryaev (1992).…”