Higher-order moments of Markov switching bilinear models‎: ‎theory and‎ ‎empirical evidence

Document Type : Original Article

Author

Abdelouahab Bibi

Department of Mathematics, University Fréres Mentouri Constantine 1, Constantine, Algeria

10.22067/smps.2025.94345.1049

Abstract

In this paper, we consider a Markov-switching bilinear process  (MS-BL) that exhibits rich dynamic behavior and plays an important role in modeling non-Gaussian data characterized by structural breaks. In such models, the parameters depend on an unobservable (hidden) Markov chain with a finite state space. Although numerous recent studies have focused on the statistical aspects of Markov-switching models, systematic investigations of the probabilistic properties of this class of nonlinear models remain relatively scarce. So, we derive conditions for stationarity and compute the moments of the process up to the third order. Our analysis reveals that the conditions ensuring local stationarity within each regime of the observed process are neither sufficient nor necessary. Furthermore, we show that the second-order structure of the process is analogous to that of a Markov-switching  ARMA (MS-ARMA) model with an additional uncorrelated white noise component. Therefore, the examination of higher-order moments becomes essential to distinguish between (locally) linear and nonlinear models. To illustrate the practical relevance of our theoretical results, we conduct Monte Carlo simulation studies and apply the proposed model to the exchange rate of the Algerian Dinar against the Euro. The empirical findings indicate that the proposed approach provides a better fit and demonstrates superior performance compared to alternative models. 
 

Keywords

‎Higher-order moments

‎Markov-switching bilinear models

‎ ‎Stationarity‎

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