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Semi-Lévy driven continuous-time GARCH process

Author

Listed:
  • Mohammadi, M.
  • Rezakhah, S.
  • Modarresi, N.

Abstract

Continuous-time GARCH (COGARCH) processes are one of the influential and successful models in financial data analysis. In contrast to such stationary process, in this paper we study a class of COGARCH processes driven by semi-Lévy process (SL-COGARCH) that has periodically correlated (PC) increments. Under sufficient conditions the strictly periodically stationarity of the state and volatility processes are shown. We verify that the increments with constant length of the SL-COGARCH process constitute a discrete-time PC process. To justify this property, we use simulations of the SL-COGARCH(1,3) process and evaluate its increments. Then we provide the sample spectral coherence test to show the PC behavior of this discrete-time process. We apply the SL-COGARCH(2,2) process to the Dow Jones Industrial Average indices and show that this model provides better prediction of the squared log returns in compare to the retrieved Lévy driven COGARCH method.

Suggested Citation

  • Mohammadi, M. & Rezakhah, S. & Modarresi, N., 2020. "Semi-Lévy driven continuous-time GARCH process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 557(C).
    • Handle: RePEc:eee:phsmap:v:557:y:2020:i:c:s037843712030443x
    DOI: 10.1016/j.physa.2020.124855
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    References listed on IDEAS

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