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Long memory in stock market volatility and the volatility-in-mean effect: the FIEGARCH-M model


  • Bent Jesper Christensen

    () (University of Aarhus and CREATES)

  • Jie Zhu

    () (University of Aarhus and CREATES)

  • Morten Ørregaard Nielsen

    () (Queen's University and CREATES)


We extend the fractionally integrated exponential GARCH (FIEGARCH) model for daily stock return data with long memory in return volatility of Bollerslev and Mikkelsen (1996) by introducing a possible volatility-in-mean effect. To avoid that the long memory property of volatility carries over to returns, we consider a filtered FIEGARCH-in-mean (FIEGARCH-M) effect in the return equation. The filtering of the volatility-in-mean component thus allows the co-existence of long memory in volatility and short memory in returns. We present an application to the daily CRSP value-weighted cum-dividend stock index return series from 1926 through 2006 which documents the empirical relevance of our model. The volatility-in-mean effect is significant, and the FIEGARCH-M model outperforms the original FIEGARCH model and alternative GARCH-type specifications according to standard criteria.

Suggested Citation

  • Bent Jesper Christensen & Jie Zhu & Morten Ørregaard Nielsen, 2009. "Long memory in stock market volatility and the volatility-in-mean effect: the FIEGARCH-M model," Working Papers 1207, Queen's University, Department of Economics.
  • Handle: RePEc:qed:wpaper:1207

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    References listed on IDEAS

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    6. Christensen, Bent Jesper & Dahl, Christian M. & Iglesias, Emma M., 2012. "Semiparametric inference in a GARCH-in-mean model," Journal of Econometrics, Elsevier, vol. 167(2), pages 458-472.
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    11. Dahl, Christian M. & Iglesias, Emma M., 2009. "Volatility spill-overs in commodity spot prices: New empirical results," Economic Modelling, Elsevier, vol. 26(3), pages 601-607, May.
    12. Harry-Paul Vander Elst, 2015. "FloGARCH: Realizing Long Memory and Asymmetries in Returns Valitility," Working Papers ECARES ECARES 2015-12, ULB -- Universite Libre de Bruxelles.
    13. He, Zhongzhi (Lawrence) & Zhu, Jie & Zhu, Xiaoneng, 2015. "Dynamic factors and asset pricing: International and further U.S. evidence," Pacific-Basin Finance Journal, Elsevier, vol. 32(C), pages 21-39.
    14. Caporin, Massimiliano & Ranaldo, Angelo & Santucci de Magistris, Paolo, 2013. "On the predictability of stock prices: A case for high and low prices," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 5132-5146.
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    16. Dahl Christian M & Iglesias Emma, 2011. "Modeling the Volatility-Return Trade-Off When Volatility May Be Nonstationary," Journal of Time Series Econometrics, De Gruyter, vol. 3(1), pages 1-32, February.
    17. Vafiadis Nikolaos, 2015. "Forecasting Volatility and the Risk–Return Tradeoff: An Application on the Fama–French Benchmark Market Return," Journal of Time Series Econometrics, De Gruyter, vol. 7(2), pages 181-216, July.
    18. Andrew Harvey & Rutger-Jan Lange, 2015. "Modeling the Interactions between Volatility and Returns," Cambridge Working Papers in Economics 1518, Faculty of Economics, University of Cambridge.
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    24. Cevik, Emrah Ismail & Topaloğlu, Gültekin, 2014. "Volatilitede uzun hafıza ve yapısal kırılma: Borsa Istanbul örneği
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      ," MPRA Paper 71485, University Library of Munich, Germany, revised 2014.
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    More about this item


    FIEGARCH; financial leverage; GARCH; long memory; risk-return tradeoff; stock returns; volatility feedback;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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