Displaying similar documents to “Moderate deviations for stable Markov chains and regression models.”

Long memory properties and covariance structure of the EGARCH model

Donatas Surgailis, Marie-Claude Viano (2002)

ESAIM: Probability and Statistics

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The EGARCH model of Nelson [29] is one of the most successful ARCH models which may exhibit characteristic asymmetries of financial time series, as well as long memory. The paper studies the covariance structure and dependence properties of the EGARCH and some related stochastic volatility models. We show that the large time behavior of the covariance of powers of the (observed) ARCH process is determined by the behavior of the covariance of the (linear) log-volatility process; in particular,...

Number of hidden states and memory: a joint order estimation problem for Markov chains with Markov regime

Antoine Chambaz, Catherine Matias (2009)

ESAIM: Probability and Statistics

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This paper deals with order identification for Markov chains with Markov regime (MCMR) in the context of finite alphabets. We define the joint order of a MCMR process in terms of the number of states of the hidden Markov chain and the memory of the conditional Markov chain. We study the properties of penalized maximum likelihood estimators for the unknown order of an observed MCMR process, relying on information theoretic arguments. The novelty of our work relies in the joint...

Detecting abrupt changes in random fields

Antoine Chambaz (2002)

ESAIM: Probability and Statistics

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This paper is devoted to the study of some asymptotic properties of a M -estimator in a framework of detection of abrupt changes in random field’s distribution. This class of problems includes e.g. recovery of sets. It involves various techniques, including M -estimation method, concentration inequalities, maximal inequalities for dependent random variables and φ -mixing. Penalization of the criterion function when the size of the true model is unknown is performed. All the results apply...