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	マルコフスイッチング多重フラクタルモデル	カルマンフィルター
分野	時系列解析	ベイズ
系統	Process / pipeline	Bayesian methods
提唱年	2004	1960
提唱者	Luc E. Calvet	Rudolf E. Kalman
種類	Stochastic volatility model	recursive Bayesian filter
原典	Calvet, L. E., & Fisher, A. J. (2004). How to forecast long-run volatility: regime-switching and the estimation of multifractal processes. Journal of Financial Econometrics, 2(1), 49–83.	Kalman, R. E. (1960). A new approach to linear filtering and prediction problems. Journal of Basic Engineering, 82(1), 35-45.
別名	MSM, Markov-switching multifractal volatility	linear quadratic estimator, LQE, Kalman-Bucy filter, optimal recursive filter
関連	3	5
概要	The Markov-Switching Multifractal (MSM) model is a flexible framework for capturing time-varying volatility and long-memory effects in financial time series. Developed by Calvet and Fisher (2004), it combines Markov chain theory with multifractal scaling principles to generate volatility that exhibits multiple frequency components, each switching between high and low regimes. This approach is particularly effective for modeling asset returns with realistic fat tails and clustered volatility.	The Kalman filter is an optimal recursive algorithm for estimating the hidden state of a linear dynamical system from noisy measurements. At each time step it alternates between a prediction step — projecting the state forward using the system model — and an update step that corrects the prediction with the new observation, producing minimum-variance state estimates and their uncertainty in real time.