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Unconditional mean, Volatility and the Fourier-Garch representation

Author

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  • Pascalau, Razvan
  • Thomann, Christian
  • Gregoriou, Greg N.

Abstract

This paper proposes a new model called Fourier-GARCH that is a modification of the popular GARCH(1,1). This modification allows for time-varying first and second moments via means of Flexible Fourier transforms. A nice feature of this model is its ability to capture both short and long run dynamics in the volatility of the data, requiring only that the proper frequencies of the Fourier transform be specified. Several simulations show the ability of the Fourier series to approximate breaks of an unknown form, irrespective of the time or location of breaks. The paper shows that the main cause of the long run memory effect seen in stock returns is the result of a time varying first moment. In addition, the study suggests that allowing only the second moment to vary over time is not sufficient to capture the high persistence observed in lagged returns.

Suggested Citation

  • Pascalau, Razvan & Thomann, Christian & Gregoriou, Greg N., 2010. "Unconditional mean, Volatility and the Fourier-Garch representation," MPRA Paper 35932, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:35932
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    Cited by:

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    2. 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.
    3. Nazlioglu, Saban & Gupta, Rangan & Gormus, Alper & Soytas, Ugur, 2020. "Price and volatility linkages between international REITs and oil markets," Energy Economics, Elsevier, vol. 88(C).
    4. Nazlioglu, Saban & Gupta, Rangan & Bouri, Elie, 2020. "Movements in international bond markets: The role of oil prices," International Review of Economics & Finance, Elsevier, vol. 68(C), pages 47-58.
    5. Ke Yang & Langnan Chen, 2014. "Realized Volatility Forecast: Structural Breaks, Long Memory, Asymmetry, and Day-of-the-Week Effect," International Review of Finance, International Review of Finance Ltd., vol. 14(3), pages 345-392, September.

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    More about this item

    Keywords

    ARCH/GARCH; Structural change; Unconditional volatility;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G29 - Financial Economics - - Financial Institutions and Services - - - Other

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