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Modeling the Interactions between Volatility and Returns using EGARCH‐M

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  • 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.

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  • 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
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    2. Harvey, A. & Liao, Y., 2019. "Dynamic Tobit models," Cambridge Working Papers in Economics 1913, Faculty of Economics, University of Cambridge.
    3. 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.
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    5. Elisa Navarra, 2022. "Stock Market Response to Firms’ Misconduct," Working Papers ECARES 2022-40, ULB -- Universite Libre de Bruxelles.
    6. 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.
    7. 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.
    8. Fei, Tianlun & Liu, Xiaoquan, 2021. "Herding and market volatility," International Review of Financial Analysis, Elsevier, vol. 78(C).
    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. 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.
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    12. Palumbo, D., 2021. "Testing and Modelling Time Series with Time Varying Tails," Cambridge Working Papers in Economics 2111, Faculty of Economics, University of Cambridge.

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