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A novel time-varying FIGARCH model for improving volatility predictions

Author

Listed:
  • Chen, Xuehui
  • Zhu, Hongli
  • Zhang, Xinru
  • Zhao, Lutao

Abstract

The FIGARCH model has received wide attention due to its ability to capture the features of volatility long-memory persistence and clustering. The classical FIGARCH model is based on the difference scheme of Grünwald–Letnikov fractional operators. This paper introduces the new class of FIGARCH processes for improving time-varying volatility predictions. Firstly, a novel FIGARCH model based on the Caputo fractional operators (FIGARCH-C model for short) is proposed. Secondly, a quasi-maximum likelihood estimation (QMLE) is used to estimate the parameters of the FIGARCH-C(1, d, 1), the FIGARCH(1, d, 1) and GARCH(1, 1) models. Finally, we apply the three models to Brent crude oil and S&P 500 returns and provide the comparison results of the three models. The results show that the FIGARCH and FIGARCH-C models outperformed the GARCH model in capturing the long memory in volatility. It is also found that the FIGARCH-C model is more sensitive to capture the change in the volatile period.

Suggested Citation

  • Chen, Xuehui & Zhu, Hongli & Zhang, Xinru & Zhao, Lutao, 2022. "A novel time-varying FIGARCH model for improving volatility predictions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 589(C).
    • Handle: RePEc:eee:phsmap:v:589:y:2022:i:c:s0378437121008839
    DOI: 10.1016/j.physa.2021.126635
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    as
    1. Aggarwal, Reena & Inclan, Carla & Leal, Ricardo, 1999. "Volatility in Emerging Stock Markets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(1), pages 33-55, March.
    2. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
    3. Granger, Clive W. J. & Hyung, Namwon, 2004. "Occasional structural breaks and long memory with an application to the S&P 500 absolute stock returns," Journal of Empirical Finance, Elsevier, vol. 11(3), pages 399-421, June.
    4. Wang, Shin-Huei & Vasilakis, Chrysovalantis, 2013. "Recursive predictive tests for structural change of long-memory ARFIMA processes with unknown break points," Economics Letters, Elsevier, vol. 118(2), pages 389-392.
    5. Di Matteo, T. & Aste, T. & Dacorogna, M.M., 2003. "Scaling behaviors in differently developed markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 183-188.
    6. Cochran, Steven J. & Mansur, Iqbal & Odusami, Babatunde, 2012. "Volatility persistence in metal returns: A FIGARCH approach," Journal of Economics and Business, Elsevier, vol. 64(4), pages 287-305.
    7. Dacorogna, Michael M. & Muller, Ulrich A. & Nagler, Robert J. & Olsen, Richard B. & Pictet, Olivier V., 1993. "A geographical model for the daily and weekly seasonal volatility in the foreign exchange market," Journal of International Money and Finance, Elsevier, vol. 12(4), pages 413-438, August.
    8. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    9. Gajda, Janusz & Bartnicki, Grzegorz & Burnecki, Krzysztof, 2018. "Modeling of water usage by means of ARFIMA–GARCH processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 644-657.
    10. Baillie, Richard T. & Morana, Claudio, 2012. "Adaptive ARFIMA models with applications to inflation," Economic Modelling, Elsevier, vol. 29(6), pages 2451-2459.
    11. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
    12. Baillie, Richard T. & Morana, Claudio, 2009. "Modelling long memory and structural breaks in conditional variances: An adaptive FIGARCH approach," Journal of Economic Dynamics and Control, Elsevier, vol. 33(8), pages 1577-1592, August.
    13. Ahmad, B. & Alhothuali, M.S. & Alsulami, H.H. & Kirane, M. & Timoshin, S., 2015. "On a time fractional reaction diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 199-204.
    14. Liu, Hsiang-Hsi, 2012. "Interrelationships among the Taiwanese, Japanese and Korean TFT-LCD panel industry stock market indexes: An application of the trivariate FIEC–FIGARCH model," Economic Modelling, Elsevier, vol. 29(6), pages 2724-2733.
    15. Zhao, Lu-Tao & Liu, Kun & Duan, Xin-Lei & Li, Ming-Fang, 2019. "Oil price risk evaluation using a novel hybrid model based on time-varying long memory," Energy Economics, Elsevier, vol. 81(C), pages 70-78.
    16. Jarque, Carlos M. & Bera, Anil K., 1980. "Efficient tests for normality, homoscedasticity and serial independence of regression residuals," Economics Letters, Elsevier, vol. 6(3), pages 255-259.
    17. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    18. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    19. Beine, Michel & Benassy-Quere, Agnes & Lecourt, Christelle, 2002. "Central bank intervention and foreign exchange rates: new evidence from FIGARCH estimations," Journal of International Money and Finance, Elsevier, vol. 21(1), pages 115-144, February.
    20. Belkhouja, Mustapha & Boutahary, Mohamed, 2011. "Modeling volatility with time-varying FIGARCH models," Economic Modelling, Elsevier, vol. 28(3), pages 1106-1116, May.
    21. 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.
    22. Shi, Yanlin & Ho, Kin-Yip, 2015. "Modeling high-frequency volatility with three-state FIGARCH models," Economic Modelling, Elsevier, vol. 51(C), pages 473-483.
    23. Biage, Milton, 2019. "Analysis of shares frequency components on daily value-at-risk in emerging and developed markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 532(C).
    24. Narayan, Paresh Kumar & Narayan, Seema, 2007. "Modelling oil price volatility," Energy Policy, Elsevier, vol. 35(12), pages 6549-6553, December.
    25. Bentes, Sonia R., 2015. "Forecasting volatility in gold returns under the GARCH, IGARCH and FIGARCH frameworks: New evidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 355-364.
    26. Kang, Sang Hoon & Kang, Sang-Mok & Yoon, Seong-Min, 2009. "Forecasting volatility of crude oil markets," Energy Economics, Elsevier, vol. 31(1), pages 119-125, January.
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