Leírás
Abstract:
In time series analysis, many efforts have been made to define non-linear models compatible
with the notion of stationarity and for which various limit theorems can be applied for
statistical inference. In this sense, Markov chains techniques are widely used to study the stability properties of many autoregressive processes.
In this talk, we will discuss the possibility to include exogenous covariates in this kind of dynamical systems. Though fundamental for practical applications, inclusion of exogenous
covariates in autoregressive processes is far from being well understood.
We will present some stability criteria for some Markov chains models in random environments that can be useful to tackle these issues.
Two main approaches will be discussed. The first one concerns the extension of a classical drift/small set criterion. For some classical observation-driven models found in the literature, small sets theory is not applicable. We will then present a second criterion to circumvent this problem. Both cases are based on suitable coupling methods in order to control the loss of memory of the iterates of the chain in term of either the total variation or Wasserstein type distances.
Numerous examples for which the theory applies will be presented.