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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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    as
    1. Yu, Jun, 2005. "On leverage in a stochastic volatility model," Journal of Econometrics, Elsevier, vol. 127(2), pages 165-178, August.
    2. Manabu Asai & Michael McAleer, 2009. "Multivariate stochastic volatility, leverage and news impact surfaces," Econometrics Journal, Royal Economic Society, vol. 12(2), pages 292-309, July.
    3. Neil Shephard & Kevin Sheppard, 2010. "Realising the future: forecasting with high-frequency-based volatility (HEAVY) models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(2), pages 197-231.
    4. Diebold, Francis X & Mariano, Roberto S, 1995. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, pages 253-263.
    5. Bertrand Candelon & Gilbert Colletaz & Christophe Hurlin & Sessi Tokpavi, 2011. "Backtesting Value-at-Risk: A GMM Duration-Based Test," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 9(2), pages 314-343, Spring.
    6. Roman Liesenfeld & Jean-Francois Richard, 2006. "Classical and Bayesian Analysis of Univariate and Multivariate Stochastic Volatility Models," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 335-360.
    7. Martens, Martin & van Dijk, Dick & de Pooter, Michiel, 2009. "Forecasting S&P 500 volatility: Long memory, level shifts, leverage effects, day-of-the-week seasonality, and macroeconomic announcements," International Journal of Forecasting, Elsevier, vol. 25(2), pages 282-303.
    8. David E. Allen & Michael McAleer & Marcel Scharth, 2009. "Realized Volatility Risk," CARF F-Series CARF-F-197, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Jan 2010.
    9. Manabu Asai & Michael McAleer, 2011. "Alternative Asymmetric Stochastic Volatility Models," Econometric Reviews, Taylor & Francis Journals, vol. 30(5), pages 548-564, October.
    10. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility: A Review," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 145-175.
    11. Pong, Shiuyan & Shackleton, Mark B. & Taylor, Stephen J. & Xu, Xinzhong, 2004. "Forecasting currency volatility: A comparison of implied volatilities and AR(FI)MA models," Journal of Banking & Finance, Elsevier, vol. 28(10), pages 2541-2563, October.
    12. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
    13. Peter Christoffersen & Denis Pelletier, 2003. "Backtesting Value-at-Risk: A Duration-Based Approach," CIRANO Working Papers 2003s-05, CIRANO.
    14. Michael McAleer & Marcelo Medeiros, 2008. "Realized Volatility: A Review," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 10-45.
    15. Ole E. Barndorff-Nielsen & Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, pages 253-280.
    16. Charles Bos & Neil Shephard, 2006. "Inference for Adaptive Time Series Models: Stochastic Volatility and Conditionally Gaussian State Space Form," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 219-244.
    17. Bertrand Candelon & Gilbert Colletaz & Christophe Hurlin & Sessi Tokpavi, 2011. "Backtesting Value-at-Risk: A GMM Duration-Based Test," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 9(2), pages 314-343, Spring.
    18. 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.
    19. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, pages 347-370.
    20. Danielsson, Jon, 1994. "Stochastic volatility in asset prices estimation with simulated maximum likelihood," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 375-400.
    21. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2006. "Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise," Economics Papers 2006-W03, Economics Group, Nuffield College, University of Oxford.
    22. McAleer, Michael, 2005. "Automated Inference And Learning In Modeling Financial Volatility," Econometric Theory, Cambridge University Press, pages 232-261.
    23. Bollerslev, Tim & Ole Mikkelsen, Hans, 1996. "Modeling and pricing long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 73(1), pages 151-184, July.
    24. Tim Bollerslev & Julia Litvinova & George Tauchen, 2006. "Leverage and Volatility Feedback Effects in High-Frequency Data," Journal of Financial Econometrics, Society for Financial Econometrics, pages 353-384.
    25. Manabu Asai & Michael McAleer, 2005. "Dynamic Asymmetric Leverage in Stochastic Volatility Models," Econometric Reviews, Taylor & Francis Journals, vol. 24(3), pages 317-332.
    26. Chernov, Mikhail & Ronald Gallant, A. & Ghysels, Eric & Tauchen, George, 2003. "Alternative models for stock price dynamics," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 225-257.
    27. Tim Bollerslev & Natalia Sizova & George Tauchen, 2011. "Volatility in Equilibrium: Asymmetries and Dynamic Dependencies," Review of Finance, European Finance Association, vol. 16(1), pages 31-80.
    28. Bent Nielsen, 2008. "Power of Tests for Unit Roots in the Presence of a Linear Trend," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, pages 619-644.
    29. Bertrand Candelon & Gilbert Colletaz & Christophe Hurlin & Sessi Tokpavi, 2011. "Backtesting Value-at-Risk: A GMM Duration-Based Test," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 9(2), pages 314-343, Spring.
    30. Bollerslev, Tim & Zhou, Hao, 2002. "Estimating stochastic volatility diffusion using conditional moments of integrated volatility," Journal of Econometrics, Elsevier, vol. 109(1), pages 33-65, July.
    31. Koopman, Siem Jan & Jungbacker, Borus & Hol, Eugenie, 2005. "Forecasting daily variability of the S&P 100 stock index using historical, realised and implied volatility measurements," Journal of Empirical Finance, Elsevier, vol. 12(3), pages 445-475, June.
    32. Peter Hansen & Jeremy Large & Asger Lunde, 2008. "Moving Average-Based Estimators of Integrated Variance," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 79-111.
    33. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, pages 134-144.
    34. Todorov, Viktor, 2009. "Estimation of continuous-time stochastic volatility models with jumps using high-frequency data," Journal of Econometrics, Elsevier, vol. 148(2), pages 131-148, February.
    35. Keith Kuester & Stefan Mittnik & Marc S. Paolella, 2006. "Value-at-Risk Prediction: A Comparison of Alternative Strategies," Journal of Financial Econometrics, Society for Financial Econometrics, pages 53-89.
    36. Zhang, Lan & Mykland, Per A. & Ait-Sahalia, Yacine, 2005. "A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data," Journal of the American Statistical Association, American Statistical Association, pages 1394-1411.
    37. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise," Econometrica, Econometric Society, vol. 76(6), pages 1481-1536, November.
    38. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    39. Wiggins, James B., 1987. "Option values under stochastic volatility: Theory and empirical estimates," Journal of Financial Economics, Elsevier, pages 351-372.
    40. Bandi, Federico M. & Russell, Jeffrey R., 2011. "Market microstructure noise, integrated variance estimators, and the accuracy of asymptotic approximations," Journal of Econometrics, Elsevier, vol. 160(1), pages 145-159, January.
    41. Harvey, Andrew C & Shephard, Neil, 1996. "Estimation of an Asymmetric Stochastic Volatility Model for Asset Returns," Journal of Business & Economic Statistics, American Statistical Association, pages 429-434.
    42. Bollerslev, Tim & Zhou, Hao, 2006. "Volatility puzzles: a simple framework for gauging return-volatility regressions," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 123-150.
    43. Willem H. Buiter & Anne C. Sibert, 2003. "Cross-Border Tax Externalities: Are Budget Deficits too Small?," Levine's Bibliography 666156000000000430, UCLA Department of Economics.
    44. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, pages 42-55.
    45. Liesenfeld, Roman & Richard, Jean-Francois, 2003. "Univariate and multivariate stochastic volatility models: estimation and diagnostics," Journal of Empirical Finance, Elsevier, vol. 10(4), pages 505-531, September.
    46. Fulvio Corsi, 2009. "A Simple Approximate Long-Memory Model of Realized Volatility," Journal of Financial Econometrics, Society for Financial Econometrics, pages 174-196.
    47. Peter Christoffersen, 2004. "Backtesting Value-at-Risk: A Duration-Based Approach," Journal of Financial Econometrics, Society for Financial Econometrics, pages 84-108.
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    Citations

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    Cited by:

    1. Manabu Asai & Michael McAleer & Marcelo C. Medeiros, 2010. "Asymmetry and Long Memory in Volatility Modelling," Working Papers in Economics 10/60, University of Canterbury, Department of Economics and Finance.
    2. Shelton Peiris & Manabu Asai & Michael McAleer, 2016. "Estimating and Forecasting Generalized Fractional Long Memory Stochastic Volatility Models," Tinbergen Institute Discussion Papers 16-044/III, Tinbergen Institute.
    3. 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.
    4. repec:wly:jfutmk:v:37:y:2017:i:11:p:1141-1152 is not listed on IDEAS
    5. Manabu Asai & Chia-Lin Chang & Michael McAleer, 2016. "Realized Matrix-Exponential Stochastic Volatility with Asymmetry, Long Memory and Spillovers," Tinbergen Institute Discussion Papers 16-076/III, Tinbergen Institute.
    6. 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.
    7. Manabu Asai & Michael McAleer, 2016. "A Multivariate Asymmetric Long Memory Conditional Volatility Model with X, Regularity and Asymptotics," Tinbergen Institute Discussion Papers 16-065/III, Tinbergen Institute.
    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, 2016. "A Multivariate Asymmetric Long Memory Conditional Volatility Model with X, Regularity and Asymptotics," Tinbergen Institute Discussion Papers 16-065/III, Tinbergen Institute.
    10. Manabu Asai & Chia-Lin Chang & Michael McAleer, 2017. "Realized Stochastic Volatility with General Asymmetry and Long Memory," Tinbergen Institute Discussion Papers 17-038/III, Tinbergen Institute.
    11. Carl Lönnbark, 2016. "Asymmetry with respect to the memory in stock market volatilities," Empirical Economics, Springer, vol. 50(4), pages 1409-1419, June.
    12. 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.
    13. Asai, M. & McAleer, M.J. & Peiris, S., 2017. "Realized Stochastic Volatility Models with Generalized Gegenbauer Long Memory," Econometric Institute Research Papers EI2017-29, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    14. Shelton Peiris & Manabu Asai & Michael McAleer, 2016. "Estimating and forecasting generalized fractional Long memory stochastic volatility models," Documentos de Trabajo del ICAE 2016-08, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    15. repec:eee:eneeco:v:67:y:2017:i:c:p:315-327 is not listed on IDEAS
    16. 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, pages 436-456.
    17. 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.
    18. 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.
    19. 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.
    20. 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.
    21. 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.
    22. Kim, Min Seong & Sun, Yixiao & Yang, Jingjing, 2017. "A fixed-bandwidth view of the pre-asymptotic inference for kernel smoothing with time series data," Journal of Econometrics, Elsevier, vol. 197(2), pages 298-322.
    23. 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.
    24. Gagnon, Marie-Hélène & Power, Gabriel J. & Toupin, Dominique, 2016. "International stock market cointegration under the risk-neutral measure," International Review of Financial Analysis, Elsevier, pages 243-255.
    25. 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.

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