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Asymmetry and Long Memory in Volatility Modelling

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Abstract

A wide variety of conditional and stochastic variance models has been used to estimate latent volatility (or risk). In this paper, we propose a new long memory asymmetric volatility model which captures more flexible asymmetric patterns as compared with several existing models. We extend the new specification to realized volatility by taking account of measurement errors, and use the Efficient Importance Sampling technique to estimate the model. As an empirical example, we apply the new model to the realized volatility of S&P500 to show that the new specification of asymmetry significantly improves the goodness of fit, and that the out-of-sample forecasts and Value-at-Risk (VaR) thresholds are satisfactory. Overall, the results of the out-of-sample forecasts show the adequacy of the new asymmetric and long memory volatility model for the period including the global financial crisis.

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  • Manabu Asai & Michael McAleer & Marcelo C. Medeiros, 2011. "Asymmetry and Long Memory in Volatility Modelling," Documentos de Trabajo del ICAE 2011-29, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
  • Handle: RePEc:ucm:doicae:1129
    Note: The authors are most grateful to a Co-Editor, Associate Editor and two referees for very helpful comments and suggestions, and Marcel Scharth for efficient research assistance. For financial support, the first author acknowledges the Japan Ministry of Education, Culture, Sports, Science and Technology, Japan Society for the Promotion of Science, and Australian Academy of Science, the second author is most grateful to the Australian Research Council, National Science Council, Taiwan, and Japan Society for the Promotion of Science, and the third author wishes to acknowledge CNPq, Brazil.
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    Cited by:

    1. Asai, M. & McAleer, M.J., 2016. "A Multivariate Asymmetric Long Memory Conditional Volatility Model with X, Regularity and Asymptotics," Econometric Institute Research Papers EI2016-34, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    2. Asai, Manabu & McAleer, Michael, 2015. "Leverage and feedback effects on multifactor Wishart stochastic volatility for option pricing," Journal of Econometrics, Elsevier, vol. 187(2), pages 436-446.
    3. Shelton Peiris & Manabu Asai & Michael McAleer, 2017. "Estimating and Forecasting Generalized Fractional Long Memory Stochastic Volatility Models," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 10(4), pages 1-16, December.
    4. Gagnon, Marie-Hélène & Power, Gabriel J. & Toupin, Dominique, 2016. "International stock market cointegration under the risk-neutral measure," International Review of Financial Analysis, Elsevier, vol. 47(C), pages 243-255.
    5. Manabu Asai & Chia-Lin Chang & Michael McAleer, 2016. "Realized Matrix-Exponential Stochastic Volatility with Asymmetry, Long Memory and Spillovers," Documentos de Trabajo del ICAE 2016-15, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    6. Lopes Moreira Da Veiga, María Helena & Ruiz Ortega, Esther & Mao, Xiuping, 2013. "One for all : nesting asymmetric stochastic volatility models," DES - Working Papers. Statistics and Econometrics. WS ws131110, Universidad Carlos III de Madrid. Departamento de Estadística.
    7. Manabu Asai & Michael McAleer & Marcelo C. Medeiros, 2012. "Asymmetry and Long Memory in Volatility Modeling," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 10(3), pages 495-512, June.
    8. Manabu Asai & Michael McAleer, 2017. "A fractionally integrated Wishart stochastic volatility model," Econometric Reviews, Taylor & Francis Journals, vol. 36(1-3), pages 42-59, March.
    9. Manabu Asai & Michael McAleer, 2017. "Forecasting the volatility of Nikkei 225 futures," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 37(11), pages 1141-1152, November.
    10. Asai, Manabu & Chang, Chia-Lin & McAleer, Michael, 2017. "Realized stochastic volatility with general asymmetry and long memory," Journal of Econometrics, Elsevier, vol. 199(2), pages 202-212.
    11. Davide De Gaetano, 2016. "Forecast Combinations For Realized Volatility In Presence Of Structural Breaks," Departmental Working Papers of Economics - University 'Roma Tre' 0208, Department of Economics - University Roma Tre.
    12. repec:eee:eneeco:v:67:y:2017:i:c:p:315-327 is not listed on IDEAS
    13. Manabu Asai & Shelton Peiris & Michael McAleer, 2017. "Realized Stochastic Volatility Models with Generalized Gegenbauer Long Memory," Documentos de Trabajo del ICAE 2017-26, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    14. Carl Lönnbark, 2016. "Asymmetry with respect to the memory in stock market volatilities," Empirical Economics, Springer, vol. 50(4), pages 1409-1419, June.
    15. Ning, Cathy & Xu, Dinghai & Wirjanto, Tony S., 2015. "Is volatility clustering of asset returns asymmetric?," Journal of Banking & Finance, Elsevier, vol. 52(C), pages 62-76.
    16. Ziggel, Daniel & Berens, Tobias & Weiß, Gregor N.F. & Wied, Dominik, 2014. "A new set of improved Value-at-Risk backtests," Journal of Banking & Finance, Elsevier, vol. 48(C), pages 29-41.
    17. Wen, Fenghua & Gong, Xu & Cai, Shenghua, 2016. "Forecasting the volatility of crude oil futures using HAR-type models with structural breaks," Energy Economics, Elsevier, vol. 59(C), pages 400-413.
    18. Ho, Kin-Yip & Shi, Yanlin & Zhang, Zhaoyong, 2013. "How does news sentiment impact asset volatility? Evidence from long memory and regime-switching approaches," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 436-456.
    19. repec:eee:phsmap:v:494:y:2018:i:c:p:27-39 is not listed on IDEAS

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