IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v589y2022ics0378437121008839.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437121008839
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2021.126635?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Baillie, Richard T. & Morana, Claudio, 2012. "Adaptive ARFIMA models with applications to inflation," Economic Modelling, Elsevier, vol. 29(6), pages 2451-2459.
    3. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    4. Narayan, Paresh Kumar & Narayan, Seema, 2007. "Modelling oil price volatility," Energy Policy, Elsevier, vol. 35(12), pages 6549-6553, December.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    13. 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.
    14. Belkhouja, Mustapha & Boutahary, Mohamed, 2011. "Modeling volatility with time-varying FIGARCH models," Economic Modelling, Elsevier, vol. 28(3), pages 1106-1116, May.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. 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.
    21. 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.
    22. 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.
    23. Shi, Yanlin & Ho, Kin-Yip, 2015. "Modeling high-frequency volatility with three-state FIGARCH models," Economic Modelling, Elsevier, vol. 51(C), pages 473-483.
    24. 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).
    25. 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.
    26. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Huang, Yirong & Luo, Yi, 2024. "Forecasting conditional volatility based on hybrid GARCH-type models with long memory, regime switching, leverage effect and heavy-tail: Further evidence from equity market," The North American Journal of Economics and Finance, Elsevier, vol. 72(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wang, Yudong & Wu, Chongfeng, 2012. "Forecasting energy market volatility using GARCH models: Can multivariate models beat univariate models?," Energy Economics, Elsevier, vol. 34(6), pages 2167-2181.
    2. Wang, Yudong & Wu, Chongfeng & Yang, Li, 2016. "Forecasting crude oil market volatility: A Markov switching multifractal volatility approach," International Journal of Forecasting, Elsevier, vol. 32(1), pages 1-9.
    3. Arouri, Mohamed El Hedi & Hammoudeh, Shawkat & Lahiani, Amine & Nguyen, Duc Khuong, 2012. "Long memory and structural breaks in modeling the return and volatility dynamics of precious metals," The Quarterly Review of Economics and Finance, Elsevier, vol. 52(2), pages 207-218.
    4. Halkos, George & Tzirivis, Apostolos, 2018. "Effective energy commodities’ risk management: Econometric modeling of price volatility," MPRA Paper 90781, University Library of Munich, Germany.
    5. Wei, Yu & Wang, Yudong & Huang, Dengshi, 2010. "Forecasting crude oil market volatility: Further evidence using GARCH-class models," Energy Economics, Elsevier, vol. 32(6), pages 1477-1484, November.
    6. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    7. Halkos, George E. & Tsirivis, Apostolos S., 2019. "Effective energy commodity risk management: Econometric modeling of price volatility," Economic Analysis and Policy, Elsevier, vol. 63(C), pages 234-250.
    8. Hasanov, Akram Shavkatovich & Poon, Wai Ching & Al-Freedi, Ajab & Heng, Zin Yau, 2018. "Forecasting volatility in the biofuel feedstock markets in the presence of structural breaks: A comparison of alternative distribution functions," Energy Economics, Elsevier, vol. 70(C), pages 307-333.
    9. Charfeddine, Lanouar, 2016. "Breaks or long range dependence in the energy futures volatility: Out-of-sample forecasting and VaR analysis," Economic Modelling, Elsevier, vol. 53(C), pages 354-374.
    10. Walther, Thomas & Klein, Tony & Thu, Hien Pham & Piontek, Krzysztof, 2017. "True or spurious long memory in European non-EMU currencies," Research in International Business and Finance, Elsevier, vol. 40(C), pages 217-230.
    11. Junru Zhang & Hadrian Geri Djajadikerta & Zhaoyong Zhang, 2018. "Does Sustainability Engagement Affect Stock Return Volatility? Evidence from the Chinese Financial Market," Sustainability, MDPI, vol. 10(10), pages 1-21, September.
    12. Charfeddine, Lanouar & Ajmi, Ahdi Noomen, 2013. "The Tunisian stock market index volatility: Long memory vs. switching regime," Emerging Markets Review, Elsevier, vol. 16(C), pages 170-182.
    13. Chkili, Walid & Hammoudeh, Shawkat & Nguyen, Duc Khuong, 2014. "Volatility forecasting and risk management for commodity markets in the presence of asymmetry and long memory," Energy Economics, Elsevier, vol. 41(C), pages 1-18.
    14. Conrad, Christian & Karanasos, Menelaos & Zeng, Ning, 2011. "Multivariate fractionally integrated APARCH modeling of stock market volatility: A multi-country study," Journal of Empirical Finance, Elsevier, vol. 18(1), pages 147-159, January.
    15. Li, Gang & Li, Yong, 2015. "Forecasting copper futures volatility under model uncertainty," Resources Policy, Elsevier, vol. 46(P2), pages 167-176.
    16. Mohammadi, Hassan & Su, Lixian, 2010. "International evidence on crude oil price dynamics: Applications of ARIMA-GARCH models," Energy Economics, Elsevier, vol. 32(5), pages 1001-1008, September.
    17. Rehim Kilic, 2011. "A conditional variance tale from an emerging economy's freely floating exchange rate," Applied Economics, Taylor & Francis Journals, vol. 43(19), pages 2465-2480.
    18. Igor LEBRUN & Ludovic DOBBELAERE, 2010. "A Macro-econometric Model for the Economy of Lesotho," EcoMod2010 259600102, EcoMod.
    19. Wang, Yudong & Liu, Li & Ma, Feng & Wu, Chongfeng, 2016. "What the investors need to know about forecasting oil futures return volatility," Energy Economics, Elsevier, vol. 57(C), pages 128-139.
    20. Arouri, Mohamed El Hédi & Lahiani, Amine & Lévy, Aldo & Nguyen, Duc Khuong, 2012. "Forecasting the conditional volatility of oil spot and futures prices with structural breaks and long memory models," Energy Economics, Elsevier, vol. 34(1), pages 283-293.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:589:y:2022:i:c:s0378437121008839. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.