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...

This paper deals with the probabilistic structure and the asymptotic properties of parameters least squares estimates (LSE) for periodic GARCH (PGARCH) and for PARMA-PGARCH models. In this class of models, the parameters are allowed to switch between different regimes. Firstly, we give necessary...

In this paper, we propose a natural extension of time-invariant coefficients threshold GARCH (TGARCH) processes to periodically time-varying coefficients (PTGARCH) one. So some theoretical probabilistic properties of such models are discussed, in particular, we establish firstly necessary and...

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...

One-dimensional indexed bilinear (BL) models are widely used for modeling non Gaussian time series. Extending BL models to multidimensional indexed (spatial) SBL one, yields a novel class of models which are capable of taking into account the important characteristic of non Gaussianity and...

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....