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

Definitions and state-space modeling (Dynamic statistical models with hidden variables, Tutorial 1)

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. Definitions and state-space modeling (Dynamic statistical models with hidden variables, Tutorial 1)

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80回　（3days セミナー第1回）

Definitions and state-space modeling (Dynamic statistical models with hidden variables, Tutorial 1)

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

Dynamic statistical models with hidden variables　第１回

テーマ：Definitions and state-space modeling.
　　1. Reminder of stationary processes.
　　2. ARMA, Random variance and Hidden-Markov models.
　　3. State-space models.
概要：
　Stationarity is the basis of a general asymptotic theory for dependent processes. It ensures that an increasing sample goes with a same order increase of information. We propose to remind the definition of stationarity and introduce classic linear models. Then we specify hidden-Markov models that allows for rich dynamics. Finally, we highlight that many dynamic models can actually be defined as state-space models.

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.

↓Chapter1 スライド