IDEAS home Printed from https://ideas.repec.org/a/bla/jtsera/v39y2018i6p909-919.html
   My bibliography  Save this article

Modeling the Interactions between Volatility and Returns using EGARCH‐M

Author

Listed:
  • Andrew Harvey
  • Rutger‐Jan Lange

Abstract

An EGARCH‐M model, in which the logarithm of scale is driven by the score of the conditional distribution, is shown to be theoretically tractable as well as practically useful. A two‐component extension makes it possible to distinguish between the short‐ and long‐run effects of returns on volatility, and the resulting short‐ and long‐run volatility components are then allowed to have different effects on returns, with the long‐run component yielding the equity risk premium. The EGARCH formulation allows for more flexibility in the asymmetry of the volatility response (leverage) than standard GARCH models and suggests that, for weekly observations on two major stock market indices, the short‐term response is close to being anti‐symmetric.

Suggested Citation

  • Andrew Harvey & Rutger‐Jan Lange, 2018. "Modeling the Interactions between Volatility and Returns using EGARCH‐M," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(6), pages 909-919, November.
    • Handle: RePEc:bla:jtsera:v:39:y:2018:i:6:p:909-919
    DOI: 10.1111/jtsa.12419
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/jtsa.12419
    Download Restriction: no
    File URL: https://libkey.io/10.1111/jtsa.12419?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
    ---><---

    References listed on IDEAS

    as
    1. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-131, February.
    2. Asger Lunde & Peter R. Hansen, 2005. "A forecast comparison of volatility models: does anything beat a GARCH(1,1)?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(7), pages 873-889.
    3. Robert F. Engle & Jose Gonzalo Rangel, 2008. "The Spline-GARCH Model for Low-Frequency Volatility and Its Global Macroeconomic Causes," The Review of Financial Studies, Society for Financial Studies, vol. 21(3), pages 1187-1222, May.
    4. Campbell, John Y. & Hentschel, Ludger, 1992. "No news is good news *1: An asymmetric model of changing volatility in stock returns," Journal of Financial Economics, Elsevier, vol. 31(3), pages 281-318, June.
    5. Turner, Christopher M. & Startz, Richard & Nelson, Charles R., 1989. "A Markov model of heteroskedasticity, risk, and learning in the stock market," Journal of Financial Economics, Elsevier, vol. 25(1), pages 3-22, November.
    6. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    7. Creal, Drew & Koopman, Siem Jan & Lucas, André, 2011. "A Dynamic Multivariate Heavy-Tailed Model for Time-Varying Volatilities and Correlations," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(4), pages 552-563.
    8. Harvey,Andrew C., 2013. "Dynamic Models for Volatility and Heavy Tails," Cambridge Books, Cambridge University Press, number 9781107034723.
    9. Tata Subba Rao & Granville Tunnicliffe Wilson & Andrew Harvey & Rutger-Jan Lange, 2017. "Volatility Modeling with a Generalized t Distribution," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(2), pages 175-190, March.
    10. Christensen, Bent Jesper & Nielsen, Morten Ørregaard & Zhu, Jie, 2010. "Long memory in stock market volatility and the volatility-in-mean effect: The FIEGARCH-M Model," Journal of Empirical Finance, Elsevier, vol. 17(3), pages 460-470, June.
    11. Panayiotis Theodossiou & Christos S. Savva, 2016. "Skewness and the Relation Between Risk and Return," Management Science, INFORMS, vol. 62(6), pages 1598-1609, June.
    12. Poon, Ser-Huang & Taylor, Stephen J., 1992. "Stock returns and volatility: An empirical study of the UK stock market," Journal of Banking & Finance, Elsevier, vol. 16(1), pages 37-59, February.
    13. Tobias Adrian & Joshua Rosenberg, 2008. "Stock Returns and Volatility: Pricing the Short‐Run and Long‐Run Components of Market Risk," Journal of Finance, American Finance Association, vol. 63(6), pages 2997-3030, December.
    14. repec:bla:jfinan:v:53:y:1998:i:2:p:575-603 is not listed on IDEAS
    15. Chou, Ray Yeutien, 1988. "Volatility Persistence and Stock Valuations: Some Empirical Evidence Using Garch," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 3(4), pages 279-294, October-D.
    16. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    17. Harvey,Andrew C., 2013. "Dynamic Models for Volatility and Heavy Tails," Cambridge Books, Cambridge University Press, number 9781107630024.
    18. Harvey, Andrew & Sucarrat, Genaro, 2014. "EGARCH models with fat tails, skewness and leverage," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 320-338.
    19. French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, vol. 19(1), pages 3-29, September.
    20. Hong, Eun Pyo, 1991. "The autocorrelation structure for the GARCH-M process," Economics Letters, Elsevier, vol. 37(2), pages 129-132, October.
    21. Lanne, Markku & Saikkonen, Pentti, 2006. "Why is it so difficult to uncover the risk-return tradeoff in stock returns?," Economics Letters, Elsevier, vol. 92(1), pages 118-125, July.
    22. Bekaert, Geert & Wu, Guojun, 2000. "Asymmetric Volatility and Risk in Equity Markets," The Review of Financial Studies, Society for Financial Studies, vol. 13(1), pages 1-42.
    23. Engle, Robert F & Lilien, David M & Robins, Russell P, 1987. "Estimating Time Varying Risk Premia in the Term Structure: The Arch-M Model," Econometrica, Econometric Society, vol. 55(2), pages 391-407, March.
    24. Drew Creal & Siem Jan Koopman & André Lucas, 2013. "Generalized Autoregressive Score Models With Applications," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(5), pages 777-795, August.
    25. repec:bla:jfinan:v:44:y:1989:i:5:p:1115-53 is not listed on IDEAS
    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. Harvey, Andrew & Palumbo, Dario, 2023. "Score-driven models for realized volatility," Journal of Econometrics, Elsevier, vol. 237(2).
    2. Michel Ferreira Cardia Haddad & Szabolcs Blazsek & Philip Arestis & Franz Fuerst & Hsia Hua Sheng, 2023. "The two-component Beta-t-QVAR-M-lev: a new forecasting model," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 37(4), pages 379-401, December.
    3. Buccheri, Giuseppe & Corsi, Fulvio & Flandoli, Franco & Livieri, Giulia, 2021. "The continuous-time limit of score-driven volatility models," Journal of Econometrics, Elsevier, vol. 221(2), pages 655-675.
    4. Astrid Ayala & Szabolcs Blazsek & Adrian Licht, 2022. "Score-driven stochastic seasonality of the Russian rouble: an application case study for the period of 1999 to 2020," Empirical Economics, Springer, vol. 62(5), pages 2179-2203, May.
    5. Linton, Oliver & Wu, Jianbin, 2020. "A coupled component DCS-EGARCH model for intraday and overnight volatility," Journal of Econometrics, Elsevier, vol. 217(1), pages 176-201.
    6. Harvey, Andew & Liao, Yin, 2023. "Dynamic Tobit models," Econometrics and Statistics, Elsevier, vol. 26(C), pages 72-83.
    7. Elisa Navarra, 2022. "Stock Market Response to Firms’ Misconduct," Working Papers ECARES 2022-40, ULB -- Universite Libre de Bruxelles.
    8. Ayala Astrid & Blazsek Szabolcs & Escribano Alvaro, 2023. "Anticipating extreme losses using score-driven shape filters," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 27(4), pages 449-484, September.
    9. Ciarreta, Aitor & Pizarro-Irizar, Cristina & Zarraga, Ainhoa, 2020. "Renewable energy regulation and structural breaks: An empirical analysis of Spanish electricity price volatility," Energy Economics, Elsevier, vol. 88(C).
    10. Fei, Tianlun & Liu, Xiaoquan, 2021. "Herding and market volatility," International Review of Financial Analysis, Elsevier, vol. 78(C).
    11. Palumbo, D., 2021. "Testing and Modelling Time Series with Time Varying Tails," Cambridge Working Papers in Economics 2111, Faculty of Economics, University of Cambridge.
    12. Harvey, A. & Liao, Y., 2019. "Dynamic Tobit models," Cambridge Working Papers in Economics 1913, Faculty of Economics, University of Cambridge.
    13. Xu, Qifa & Chen, Lu & Jiang, Cuixia & Yu, Keming, 2020. "Mixed data sampling expectile regression with applications to measuring financial risk," Economic Modelling, Elsevier, vol. 91(C), pages 469-486.

    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. 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.
    2. Yueh-Neng Lin & Ken Hung, 2008. "Is Volatility Priced?," Annals of Economics and Finance, Society for AEF, vol. 9(1), pages 39-75, May.
    3. Dimitrios Koutmos, 2015. "Is there a Positive Risk†Return Tradeoff? A Forward†Looking Approach to Measuring the Equity Premium," European Financial Management, European Financial Management Association, vol. 21(5), pages 974-1013, November.
    4. Lundblad, Christian, 2007. "The risk return tradeoff in the long run: 1836-2003," Journal of Financial Economics, Elsevier, vol. 85(1), pages 123-150, July.
    5. Ghysels, Eric & Santa-Clara, Pedro & Valkanov, Rossen, 2005. "There is a risk-return trade-off after all," Journal of Financial Economics, Elsevier, vol. 76(3), pages 509-548, June.
    6. Bollerslev, Tim & Engle, Robert F. & Nelson, Daniel B., 1986. "Arch models," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 49, pages 2959-3038, Elsevier.
    7. Torben G. Andersen & Tim Bollerslev & Peter F. Christoffersen & Francis X. Diebold, 2005. "Volatility Forecasting," PIER Working Paper Archive 05-011, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    8. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.
    9. James Morley, 2000. "Is There a Positive Intertemporal Tradeoff Between Risk and Return After All?," Econometric Society World Congress 2000 Contributed Papers 0915, Econometric Society.
    10. Patricia Chelley-Steeley & James Steeley, 2005. "The leverage effect in the UK stock market," Applied Financial Economics, Taylor & Francis Journals, vol. 15(6), pages 409-423.
    11. Christensen, Bent Jesper & Nielsen, Morten Ørregaard & Zhu, Jie, 2010. "Long memory in stock market volatility and the volatility-in-mean effect: The FIEGARCH-M Model," Journal of Empirical Finance, Elsevier, vol. 17(3), pages 460-470, June.
    12. 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.
    13. Claudeci Da Silva & Hugo Agudelo Murillo & Joaquim Miguel Couto, 2014. "Early Warning Systems: Análise De Ummodelo Probit De Contágio De Crise Dos Estados Unidos Para O Brasil(2000-2010)," Anais do XL Encontro Nacional de Economia [Proceedings of the 40th Brazilian Economics Meeting] 110, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].
    14. Linton, Oliver & Wu, Jianbin, 2020. "A coupled component DCS-EGARCH model for intraday and overnight volatility," Journal of Econometrics, Elsevier, vol. 217(1), pages 176-201.
    15. Thuy Thi Thu Truong & Jungmu Kim, 2019. "Premiums for Non-Sustainable and Sustainable Components of Market Volatility: Evidence from the Korean Stock Market," Sustainability, MDPI, vol. 11(18), pages 1-15, September.
    16. Turan Bali & Kamil Yilmaz, 2009. "The Intertemporal Relation between Expected Return and Risk on Currency," Koç University-TUSIAD Economic Research Forum Working Papers 0909, Koc University-TUSIAD Economic Research Forum, revised Nov 2009.
    17. Charles, Amélie & Darné, Olivier, 2017. "Forecasting crude-oil market volatility: Further evidence with jumps," Energy Economics, Elsevier, vol. 67(C), pages 508-519.
    18. 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.
    19. Xing, Xuejing & Howe, John S., 2003. "The empirical relationship between risk and return: evidence from the UK stock market," International Review of Financial Analysis, Elsevier, vol. 12(3), pages 329-346.
    20. Kim, Dongcheol & Kon, Stanley J., 1999. "Structural change and time dependence in models of stock returns," Journal of Empirical Finance, Elsevier, vol. 6(3), pages 283-308, September.

    More about this item

    Statistics

    Access and download statistics

    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:bla:jtsera:v:39:y:2018:i:6:p:909-919. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782 .

    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.