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Revisiting the Kurtosis of Stationary Processes with Applications to Volatility Models

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  • Shelton Peiris
  • Tim Swartz

Abstract

This paper establishes a number of new results on kurtosis of stationary processes as they play important roles in modelling and applications in ï¬ nancial time series. Some examples from ARCH and GARCH models are added to illustrate the usefulness and applicability of these newresults.JELClassiï¬ cation Numbers: C18, C49, C58, C59.AMS Subject Classiï¬ cation: Primary 62M10; Secondary 60G10, 91B84.Keywords: Time series, Autoregression, Serial Correlation, Kurtosis,Moments, ARCH, GARCH, Stationarity, ARMA, Volatility, Heteroscedasticity.

Suggested Citation

  • Shelton Peiris & Tim Swartz, 2020. "Revisiting the Kurtosis of Stationary Processes with Applications to Volatility Models," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 9(2), pages 1-1.
    • Handle: RePEc:spt:stecon:v:9:y:2020:i:2:f:9_2_1
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    References listed on IDEAS

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    1. Thavaneswaran, A. & Appadoo, S.S. & Peiris, S., 2005. "Forecasting volatility," Statistics & Probability Letters, Elsevier, vol. 75(1), pages 1-10, November.
    2. He, Changli & Teräsvirta, Timo & Malmsten, Hans, 1999. "Fourth Moment Structure of a Family of First-Order Exponential GARCH Models," SSE/EFI Working Paper Series in Economics and Finance 345, Stockholm School of Economics.
    3. He, Changli & Teräsvirta, Timo, 1999. "FOURTH MOMENT STRUCTURE OF THE GARCH(p,q) PROCESS," Econometric Theory, Cambridge University Press, vol. 15(6), pages 824-846, December.
    4. Bai, Xuezheng & Russell, Jeffrey R. & Tiao, George C., 2003. "Kurtosis of GARCH and stochastic volatility models with non-normal innovations," Journal of Econometrics, Elsevier, vol. 114(2), pages 349-360, June.
    5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    6. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    More about this item

    Keywords

    time series; autoregression; serial correlation; kurtosis; moments; arch; garch; stationarity; arma; volatility; heteroscedasticity.;
    All these keywords.

    JEL classification:

    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C49 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Other
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • C59 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Other

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