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A Student t-mixture autoregressive model with applications to heavy-tailed financial data

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  • C. S. Wong
  • W. S. Chan
  • P. L. Kam

Abstract

We introduce the class of Student t-mixture autoregressive models, which is promising for financial time series modelling. The model is able to capture serial correlations, time-varying means and volatilities, and the shape of the conditional distributions can be time varied from short-tailed to long-tailed, or from unimodal to multimodal. The use of t-distributed errors in each component of the model allows conditional leptokurtic distributions that account for the commonly observed excess unconditional kurtosis in financial data. Methods of parameter estimation and model selection are given. Finally, the proposed modelling procedure is illustrated through a real example. Copyright 2009, Oxford University Press.

Suggested Citation

  • C. S. Wong & W. S. Chan & P. L. Kam, 2009. "A Student t-mixture autoregressive model with applications to heavy-tailed financial data," Biometrika, Biometrika Trust, vol. 96(3), pages 751-760.
    • Handle: RePEc:oup:biomet:v:96:y:2009:i:3:p:751-760
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    File URL: http://hdl.handle.net/10.1093/biomet/asp031
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    Cited by:

    1. Mika Meitz & Daniel Preve & Pentti Saikkonen, 2023. "A mixture autoregressive model based on Student’s t–distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 52(2), pages 499-515, January.
    2. Xi, Yanhui & Peng, Hui & Qin, Yemei & Xie, Wenbiao & Chen, Xiaohong, 2015. "Bayesian analysis of heavy-tailed market microstructure model and its application in stock markets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 117(C), pages 141-153.
    3. Paul Doukhan & Konstantinos Fokianos & Joseph Rynkiewicz, 2021. "Mixtures of Nonlinear Poisson Autoregressions," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(1), pages 107-135, January.
    4. Ruili Sun & Tiefeng Ma & Shuangzhe Liu & Milind Sathye, 2019. "Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review," JRFM, MDPI, vol. 12(1), pages 1-34, March.
    5. Haas, Markus & Liu, Ji-Chun, 2015. "Theory for a Multivariate Markov--switching GARCH Model with an Application to Stock Markets," VfS Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 112855, Verein für Socialpolitik / German Economic Association.
    6. Wong, C.S., 2013. "On a constrained mixture vector autoregressive model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 93(C), pages 19-28.
    7. Wong, C.S., 2011. "Modeling Hong Kong’s stock index with the Student t-mixture autoregressive model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(7), pages 1334-1343.
    8. Chen, Yan & Yu, Wenqiang, 2020. "Setting the margins of Hang Seng Index Futures on different positions using an APARCH-GPD Model based on extreme value theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 544(C).
    9. Arifatus Solikhah & Heri Kuswanto & Nur Iriawan & Kartika Fithriasari, 2021. "Fisher’s z Distribution-Based Mixture Autoregressive Model," Econometrics, MDPI, vol. 9(3), pages 1-35, June.

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