## A Class of Switching Regimes Autoregressive Driven Processes with Exogenous Components

• In this paper we develop a data-driven mixture of vector autoregressive models with exogenous components. The process is assumed to change regimes according to an underlying Markov process. In contrast to the hidden Markov setup, we allow the transition probabilities of the underlying Markov process to depend on past time series values and exogenous variables. Such processes have potential applications to modeling brain signals. For example, brain activity at time t (measured by electroencephalograms) will can be modeled as a function of both its past values as well as exogenous variables (such as visual or somatosensory stimuli). Furthermore, we establish stationarity, geometric ergodicity and the existence of moments for these processes under suitable conditions on the parameters of the model. Such properties are important for understanding the stability properties of the model as well as deriving the asymptotic behavior of various statistics and model parameter estimators.

### Weitere Dienste

Verfasserangaben: Joseph Tadjuidje Kamgaing, Hernando Ombao, Richard A. Davis urn:nbn:de:hbz:386-kluedo-15739 Report in Wirtschaftsmathematik (WIMA Report) (115) Preprint Englisch 2008 2008 Technische Universität Kaiserslautern 23.07.2008 change point ; estimation; geometric ergodicity ; stationarity Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 510 Mathematik Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

$Rev: 13581$