Minimum distance estimation of Markov-switching bilinear processes

Abstract

ABSTRACTIn this article we introduce Markov-switching bilinear (MS-BL) process in order to model time series that exhibit structural breaks but behave (locally) strong nonlinear features. One advantage of this new class of models is its capability to take into account the important characterization of non-Gaussianity behaviour, and its ability to capture certain phenomena commonly observed in practice, such as limit cycles, self-excitation, asymmetric distribution, leptokurtosis and Taylor effect. In this class of models, which includes many popular growth curve models, the parameters are allowed to change over time according to an unobservable time-homogeneous Markov chain with finite state space. Our attention is focussed firstly on some basic issues concerning this class including sufficient conditions ensuring the existence of strictly stationarity and ergodic solutions and the existence of finite order moments. As a consequence, we find that the -structures of the process and its powers are similar to that of an ARMA with some uncorrelated innovation. Secondary, we invest the fundamental problems linked with MS-BL models, i.e. parameters estimation by a minimum distance estimator (MDE). More precisely, we provide the detail on the asymptotic properties of MDE, in particular, we discuss conditions for its consistency and asymptotic normality. Numerical experiments on simulated datasets are presented to highlight the theoretical results.