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Lionel TRUQUET (ENSAI) STATIONARITY AND ERGODICITY PROPERTIES OF NON-LINEAR AUTOREGRESSIVE PROCESSES WITH EXOGENOUS
Date: 10th of December 2020
Lionel TRUQUET (ENSAI) “Stationarity and ergodicity properties of non-linear autoregressive processes with exogenous“
While many non-linear time series models are now available in the literature, there is a recent and growing interest in developing a theoretical framework for considering non-linear dynamics that can also incorporate exogenous regressors. A particularly tricky problem for dealing with such time series models is to find some conditions for getting stationarity and ergodicity of the paths, two properties often necessary for deriving statistical properties of M estimators. In this talk, I will present two useful approaches for studying some standard time series models found in the econometrics or financial literature.
The first one is based on the study of the convergence of the backward iterations of dependent random maps. In the case of strictly exogenous regressors, I will introduce a second one, based on a coupling method for controlling the backward iterations of some Markov chains in random environments.The results will be illustrated with Garch type processes, count autoregressions and categorical time series.
Jean-Michel ZAKOIAN (CREST )
CREST and ILB
Address : ENSAE ParisTech
5, avenue Henry Le Chatelier
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