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Hidden Markov and Semi-Markov Models with Multivariate Leptokurtic-Normal Components for Robust Modeling of Daily Returns Series

Author

Listed:
  • Antonello Maruotti
  • Antonio Punzo
  • Luca Bagnato

Abstract

We introduce multivariate models for the analysis of stock market returns. Our models are developed under hidden Markov and semi-Markov settings to describe the temporal evolution of returns, whereas the marginal distribution of returns is described by a mixture of multivariate leptokurtic-normal (LN) distributions. Compared to the normal distribution, the LN has an additional parameter governing excess kurtosis and this allows us a better fit to both the distributional and dynamic properties of daily returns. We outline an expectation maximization algorithm for maximum likelihood estimation which exploits recursions developed within the hidden semi-Markov literature. As an illustration, we provide an example based on the analysis of a bivariate time series of stock market returns.

Suggested Citation

  • Antonello Maruotti & Antonio Punzo & Luca Bagnato, 2019. "Hidden Markov and Semi-Markov Models with Multivariate Leptokurtic-Normal Components for Robust Modeling of Daily Returns Series," Journal of Financial Econometrics, Oxford University Press, vol. 17(1), pages 91-117.
    • Handle: RePEc:oup:jfinec:v:17:y:2019:i:1:p:91-117.
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nby019
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    Citations

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    Cited by:

    1. Luca Bagnato & Antonio Punzo, 2021. "Unconstrained representation of orthogonal matrices with application to common principal components," Computational Statistics, Springer, vol. 36(2), pages 1177-1195, June.
    2. Antonio Punzo & Salvatore Ingrassia & Antonello Maruotti, 2021. "Multivariate hidden Markov regression models: random covariates and heavy-tailed distributions," Statistical Papers, Springer, vol. 62(3), pages 1519-1555, June.
    3. Enrique Molina‐Muñoz & Andrés Mora‐Valencia & Javier Perote, 2021. "Backtesting expected shortfall for world stock index ETFs with extreme value theory and Gram–Charlier mixtures," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(3), pages 4163-4189, July.
    4. Antonello Maruotti & Antonio Punzo, 2021. "Initialization of Hidden Markov and Semi‐Markov Models: A Critical Evaluation of Several Strategies," International Statistical Review, International Statistical Institute, vol. 89(3), pages 447-480, December.
    5. Massimo Guidolin & Manuela Pedio, 2022. "Switching Coefficients or Automatic Variable Selection: An Application in Forecasting Commodity Returns," Forecasting, MDPI, vol. 4(1), pages 1-32, February.
    6. Shanshan Qin & Zhenni Tan & Yuehua Wu, 2024. "On robust estimation of hidden semi-Markov regime-switching models," Annals of Operations Research, Springer, vol. 338(2), pages 1049-1081, July.
    7. Maruotti, Antonello & Petrella, Lea & Sposito, Luca, 2021. "Hidden semi-Markov-switching quantile regression for time series," Computational Statistics & Data Analysis, Elsevier, vol. 159(C).

    More about this item

    Keywords

    daily returns; elliptical distributions; EM algorithm; hidden Markov model; hidden semi-Markov model; kurtosis; multivariate time series;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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