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

The Kalman filter (Dynamic statistical models with hidden variables. Tutorial 2)

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

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4. The Kalman filter (Dynamic statistical models with hidden variables. Tutorial 2)

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81回　（3days セミナー第2回）

The Kalman filter (Dynamic statistical models with hidden variables. Tutorial 2)

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

Dynamic statistical models with hidden variables　第2回

テーマ：The Kalman filter
　　1. General form of the Kalman filter.
　　2. Prediction and smoothing.
　　3. Statistical inference.
概要：
　The inference method for state-space systems is the Kalman filter, which is a recursive procedure that enables to write the likelihood when the random noises of the state-space system are gaussian. We provide the recursive procedure that can be summarized as prediction equations - updating equations and show how the Kalman filter can be used for prediction. Finally, we propose a M-estimator regarding the statistical inference of 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.

↓Chapter2 スライド