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Mon, 27 Jul 2009 08:47:55 +0200Mon, 27 Jul 2009 08:47:55 +0200Mixtures of Nonparametric Autoregression, revised
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2115
We consider data generating mechanisms which can be represented as mixtures of finitely many regression or autoregression models. We propose nonparametric estimators for the functions characterizing the various mixture components based on a local quasi maximum likelihood approach and prove their consistency. We present an EM algorithm for calculating the estimates numerically which is mainly based on iteratively applying common local smoothers and discuss its convergence properties.Jürgen Franke; Jean-Pierre Stockis; Joseph Tadjuidje; W.K. Lipreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2115Mon, 27 Jul 2009 08:47:55 +0200Mixtures of Nonparametric Autoregressions
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2102
We consider data generating mechanisms which can be represented as mixtures of finitely many regression or autoregression models. We propose nonparametric estimators for the functions characterizing the various mixture components based on a local quasi maximum likelihood approach and prove their consistency. We present an EM algorithm for calculating the estimates numerically which is mainly based on iteratively applying common local smoothers and discuss its convergence properties.Jürgen Franke; Jean-Pierre Stockis; Joseph Tadjuidje; W.K. Lipreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2102Mon, 13 Jul 2009 15:52:26 +0200Quantile Sieve Estimates for Time Series
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1834
We consider the problem of estimating the conditional quantile of a time series at time \(t\) given observations of the same and perhaps other time series available at time \(t-1\). We discuss sieve estimates which are a nonparametric versions of the Koenker-Bassett regression quantiles and do not require the specification of the innovation law. We prove consistency of those estimates and illustrate their good performance for light- and heavy-tailed distributions of the innovations with a small simulation study. As an economic application, we use the estimates for calculating the value at risk of some stock price series.Jürgen Franke; Jean-Pierre Stockis; Joseph Tadjuidjepreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1834Mon, 05 Feb 2007 14:01:57 +0100A 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