In this paper, we consider the class of Markov switching bilinear processes (MS–BL) that offer remarkably rich dynamics and may be considered as an alternative to model non Gaussian data which exhibit structural changes. In these models, the parameters are allowed to depend upon a latent...

In this note, a sufficient condition is given for the existence and uniqueness of a stable causal solution for bilinear time series with time-varying coefficients; also some conditions for invertibility and the optimal prediction procedure are given. The notions of controllability, observability...

This paper studies some probabilistic properties of periodic bilinear processes. In these nonlinear models, the parameters are allowed to switch between different regimes. Stationarity and geometric ergodicity conditions (in periodic sense) are given under general and tractable assumptions....

This article establishes the strong consistency and asymptotic normality (CAN) of the quasi-maximum likelihood estimator (QMLE) for generalized autoregressive conditionally heteroscedastic (GARCH) and autoregressive moving-average (ARMA)-GARCH processes with periodically time-varying parameters....

This note examines some probabilistic properties of periodic and integrated periodic generalized autoregressive conditionally heteroskedasticitic ((I)PGARCH) processes. In these models, the parameters are allowed to switch between different regimes and thus constitute an important subclass of...

In this paper, sufficient conditions are given for the existence of a causal stable solution for general bilinear time series with time-dependent coefficients.