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An Experiment on Autoregressive and Threshold Autoregressive Models with Non-Gaussian Error with Application to Realized Volatility

Author

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  • Ziyi Zhang

    (Department of Statistics and Actuarial Science, University of Hong Kong, Hong Kong, China
    Current address: Room C, Front Portion, 2/F, No.425Z Queen’s Road West, Hong Kong.
    These authors contributed equally to this work.)

  • Wai Keung Li

    (Department of Statistics and Actuarial Science, University of Hong Kong, Hong Kong, China
    These authors contributed equally to this work.)

Abstract

This article explores the fitting of Autoregressive (AR) and Threshold AR (TAR) models with a non-Gaussian error structure. This is motivated by the problem of finding a possible probabilistic model for the realized volatility. A Gamma random error is proposed to cater for the non-negativity of the realized volatility. With many good properties, such as consistency even for non-Gaussian errors, the maximum likelihood estimate is applied. Furthermore, a non-gradient numerical Nelder–Mead method for optimization and a penalty method, introduced for the non-negative constraint imposed by the Gamma distribution, are used. In the simulation experiments, the proposed fitting method found the true model with a rather insignificant bias and mean square error (MSE), given the true AR or TAR model. The AR and TAR models with Gamma random error are then tested on empirical realized volatility data of 30 stocks, where one third of the cases are fitted quite well, suggesting that the model may have potential as a supplement for current Gaussian random error models with proper adaptation.

Suggested Citation

  • Ziyi Zhang & Wai Keung Li, 2019. "An Experiment on Autoregressive and Threshold Autoregressive Models with Non-Gaussian Error with Application to Realized Volatility," Economies, MDPI, vol. 7(2), pages 1-11, June.
    • Handle: RePEc:gam:jecomi:v:7:y:2019:i:2:p:58-:d:240654
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    References listed on IDEAS

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    1. Michael McAleer & Marcelo Medeiros, 2008. "Realized Volatility: A Review," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 10-45.
    2. Zeyu Zheng & Zhi Qiao & Tetsuya Takaishi & H Eugene Stanley & Baowen Li, 2014. "Realized Volatility and Absolute Return Volatility: A Comparison Indicating Market Risk," PLOS ONE, Public Library of Science, vol. 9(7), pages 1-10, July.
    3. Golosnoy, Vasyl & Gribisch, Bastian & Liesenfeld, Roman, 2012. "The conditional autoregressive Wishart model for multivariate stock market volatility," Journal of Econometrics, Elsevier, vol. 167(1), pages 211-223.
    4. Dimos S. Kambouroudis & David G. McMillan & Katerina Tsakou, 2016. "Forecasting Stock Return Volatility: A Comparison of GARCH, Implied Volatility, and Realized Volatility Models," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 36(12), pages 1127-1163, December.
    5. Andersen, Torben G. & Bollerslev, Tim & Lange, Steve, 1999. "Forecasting financial market volatility: Sample frequency vis-a-vis forecast horizon," Journal of Empirical Finance, Elsevier, vol. 6(5), pages 457-477, December.
    6. W. K. Li & A. I. McLeod, 1988. "Arma Modelling With Non‐Gaussian Innovations," Journal of Time Series Analysis, Wiley Blackwell, vol. 9(2), pages 155-168, March.
    7. J. Ledolter, 1979. "Inference robustness of ARIMA models under non-normality —Special application to stock price data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 26(1), pages 43-56, December.
    8. Guodong Li & Bo Guan & Wai Keung Li & Philip L. H. Yu, 2015. "Hysteretic autoregressive time series models," Biometrika, Biometrika Trust, vol. 102(3), pages 717-723.
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    Cited by:

    1. Kai-Yin Woo & Chulin Mai & Michael McAleer & Wing-Keung Wong, 2020. "Review on Efficiency and Anomalies in Stock Markets," Economies, MDPI, vol. 8(1), pages 1-51, March.
    2. Wing-Keung Wong, 2020. "Editorial Statement and Research Ideas for Efficiency and Anomalies in Stock Markets," Economies, MDPI, vol. 8(1), pages 1-4, February.

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