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.

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Author:Joseph Tadjuidje Kamgaing, Hernando Ombao, Richard A. Davis
URN (permanent link):urn:nbn:de:hbz:386-kluedo-15739
Serie (Series number):Report in Wirtschaftsmathematik (WIMA Report) (115)
Document Type:Preprint
Language of publication:English
Year of Completion:2008
Year of Publication:2008
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2008/07/23
Tag:change point; estimation; geometric ergodicity; stationarity
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011