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Smoothing in Markov switching linear and gaussian models : Applications to commodity modelization

Abstract : The work presented in this thesis focuses on Sequential Monte Carlo methods for general state space models. These procedures are used to approximate any sequence of conditional distributions of some hidden state variables given a set observations. We are particularly interested in two-filter based methods to estimate the marginal smoothing distribution of a state variable given past and future observations. We first prove convergence results for the estimators produced by all two-filter based Sequential Monte Carlo methods under weak assumptions on the hidden Markov model. Under additional strong mixing assumptions which are more restrictive but still standard in this context, we show that the constants of the deviation inequalities and the asymptotic variances are uniformly bounded in time. Then, a Conditionally Linear and Gaussian hidden Markov model is introduced to explain commodity markets regime shifts. The markets are modeled by extending the Gibson-Schwartz model on the spot price and the convenience yield. It is assumed that the dynamics of these variables is controlled by a discrete hidden Markov chain identifying the regimes. Each regime corresponds to a set of parameters driving the state space model dynamics. We propose a Monte Carlo Expectation Maximization algorithm to estimate the parameters of the model based on a two-filter method to approximate the intermediate quantity. This algorithm uses explicit marginalization (Rao Blackwellisation) of the linear states to reduce Monte Carlo variance. The algorithm performance is illustrated using Chicago Mercantile Exchange (CME) crude oil data.
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Thi Ngoc Minh Nguyen. Smoothing in Markov switching linear and gaussian models : Applications to commodity modelization. Statistics [math.ST]. Télécom ParisTech, 2016. English. ⟨NNT : 2016ENST0069⟩. ⟨tel-03689917⟩

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