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Simulated evidence on the distribution of the standardized one-step-ahead prediction errors in ARCH processes

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  • Stavros Degiannakis
  • Evdokia Xekalaki

Abstract

In statistical modelling contexts, the use of one-step-ahead prediction errors for testing hypotheses on the forecasting ability of an assumed model has been widely considered. Quite often, the testing procedure requires independence in a sequence of recursive standardized prediction errors, which cannot always be readily deduced particularly in the case of econometric modelling. In this paper, the results of a series of Monte Carlo simulations reveal that independence can be assumed to hold.

Suggested Citation

  • Stavros Degiannakis & Evdokia Xekalaki, 2007. "Simulated evidence on the distribution of the standardized one-step-ahead prediction errors in ARCH processes," Applied Financial Economics Letters, Taylor and Francis Journals, vol. 3(1), pages 31-37, January.
  • Handle: RePEc:taf:apfelt:v:3:y:2007:i:1:p:31-37
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    References listed on IDEAS

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    1. Xekalaki, Evdokia & Degiannakis, Stavros, 2005. "Evaluating volatility forecasts in option pricing in the context of a simulated options market," Computational Statistics & Data Analysis, Elsevier, vol. 49(2), pages 611-629, April.
    2. 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.
    3. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    4. Brock, W.A. & Dechert, W.D. & LeBaron, B. & Scheinkman, J.A., 1995. "A Test for Independence Based on the Correlation Dimension," Working papers 9520, Wisconsin Madison - Social Systems.
    5. Ding, Zhuanxin & Granger, Clive W. J., 1996. "Modeling volatility persistence of speculative returns: A new approach," Journal of Econometrics, Elsevier, vol. 73(1), pages 185-215, July.
    6. Engle, Robert F. & Mustafa, Chowdhury, 1992. "Implied ARCH models from options prices," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 289-311.
    7. He, Changli & Terasvirta, Timo, 1999. "Properties of moments of a family of GARCH processes," Journal of Econometrics, Elsevier, vol. 92(1), pages 173-192, September.
    8. Stavros Degiannakis & Evdokia Xekalaki, 2007. "Assessing the performance of a prediction error criterion model selection algorithm in the context of ARCH models," Applied Financial Economics, Taylor & Francis Journals, vol. 17(2), pages 149-171.
    9. Degiannakis, Stavros & Xekalaki, Evdokia, 2005. "Predictability and Model Selection in the Context of ARCH Models," MPRA Paper 80486, University Library of Munich, Germany.
    10. Karanasos, Menelaos, 1999. "The second moment and the autocovariance function of the squared errors of the GARCH model," Journal of Econometrics, Elsevier, vol. 90(1), pages 63-76, May.
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