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Mon, 12 Sep 2011 09:49:44 +0200Mon, 12 Sep 2011 09:49:44 +0200Changepoint tests for INARCH time series
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2725
In this paper, we discuss the problem of testing for a changepoint in the structure
of an integer-valued time series. In particular, we consider a test statistic
of cumulative sum (CUSUM) type for general Poisson autoregressions of order
1. We investigate the asymptotic behaviour of conditional least-squares estimates
of the parameters in the presence of a changepoint. Then, we derive the
asymptotic distribution of the test statistic under the hypothesis of no change,
allowing for the calculation of critical values. We prove consistency of the test,
i.e. asymptotic power 1, and consistency of the corresponding changepoint estimate.
As an application, we have a look at changepoint detection in daily
epileptic seizure counts from a clinical study.Jürgen Franke; Claudia Kirch; Joseph Tadjuidje Kamgaingpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2725Mon, 12 Sep 2011 09:49:44 +0200Maximum Likelihood Estimators for Markov Switching Autoregressive Processes with ARCH Component
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2146
We consider a mixture of AR-ARCH models where the switching between the basic states of the observed time series is controlled by a hidden Markov chain. Under simple conditions, we prove consistency and asymptotic normality of the maximum likelihood parameter estimates combining general results on asymptotics of Douc et al (2004) and of geometric ergodicity of Franke et al (2007).Jürgen Franke; Joseph Tadjuidje Kamgaingpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2146Mon, 19 Oct 2009 17:01:13 +0200A note on the identifiability of the conditional expectation for the mixtures of neural networks
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1832
We consider a generalized mixture of nonlinear AR models, a hidden Markov model for which the autoregressive functions are single layer feedforward neural networks. The non trivial problem of identifiability, which is usually postulated for hidden Markov models, is addressed here.Jürgen Franke; Jean-Pierre Stockis; Joseph Tadjuidje Kamgaingpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1832Fri, 12 Jan 2007 20:16:48 +0100On Geometric Ergodicity of CHARME Models
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1831
In this paper we consider a CHARME Model, a class of generalized mixture of nonlinear nonparametric AR-ARCH time series. We apply the theory of Markov models to derive asymptotic stability of this model. Indeed, the goal is to provide some sets of conditions under which our model is geometric ergodic and therefore satisfies some mixing conditions. This result can be considered as the basis toward an asymptotic theory for our model.Jürgen Franke; Jean-Pierre Stockis; Joseph Tadjuidje Kamgaingpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1831Fri, 12 Jan 2007 20:14:26 +0100