大阪大学　数理・データ科学教育研究センター
Center for Mathematical Modeling and Data Science,Osaka University

Markov-switching models (Dynamic statistical models with hidden variables, Tutorial 3)

Benjamin Poignard (CREST - Paris Dauphine University (CEREMADE))

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2. セミナー・集中講義
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4. Markov-switching models (Dynamic statistical models with hidden variables, Tutorial 3)

大阪大学 数理・データ科学セミナー 金融・保険セミナーシリーズ 第82回　（3days セミナー第3回）

Markov-switching models (Dynamic statistical models with hidden variables, Tutorial 3)

Benjamin Poignard (CREST - Paris Dauphine University (CEREMADE))

Dynamic statistical models with hidden variables　第3回

テーマ：Markov-switching models
　　1. Finite-state Markov chains and Hidden-Markov models.
　　2. Markov-switching ARMA models.
　　3. Estimation of the MS-AR(p) model.
概要：
　We first provide some definitions of Markov chains. Then we focus on the MS-ARMA(p,q) model and provide the techniques to obtain the stationarity conditions. The statistical inference for Markov-switching models is then studied, where we introduce the method to compute the likelihood together with the optimization technique: the Hamilton filter and the EM algorithm.

チュートリアルセミナー　
テーマ：Dynamic statistical models with hidden variables　
概要：Dynamic models involving hidden variables are an important family that aims at capturing the dynamic properties of dependent processes in finance. The linear state-space model, the hidden-Markov - or Markov switching (MS) - model and the stochastic volatility model are important parameterizations among this family. This modeling is intuitive and can easily be interpreted for financial time series. However, these hidden processes cause intricate statistical problems. The likelihood is generally not explicitly available, which hampers the use of the maximum likelihood method. Alternative estimation techniques were proposed to cope with these difficulties such as simulation approaches. The objective of the tutorial is to present the main model specifications, to derive their probabilistic properties and to analyse the relevant inference methods regarding such modelings.

Chapter３ スライド
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