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Simulated Evidence on the Distribution of the Standardized One-Step-Ahead Prediction Errors in ARCH Processes

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  • Degiannakis, Stavros
  • Xekalaki, Evdokia

Abstract

In statistical modeling 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 modeling. In this paper, the results of a series of Monte Carlo simulations reveal that independence can be assumed to hold.

Suggested Citation

  • Degiannakis, Stavros & Xekalaki, Evdokia, 2007. "Simulated Evidence on the Distribution of the Standardized One-Step-Ahead Prediction Errors in ARCH Processes," MPRA Paper 96326, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:96326
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    File URL: https://mpra.ub.uni-muenchen.de/96326/1/MPRA_paper_96326.pdf
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    References listed on IDEAS

    as
    1. Degiannakis, Stavros & Xekalaki, Evdokia, 2004. "Autoregressive Conditional Heteroskedasticity (ARCH) Models: A Review," MPRA Paper 80487, University Library of Munich, Germany.
    2. 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.
    3. 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.
    4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    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. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    9. Stavros Degiannakis & Evdokia Xekalaki, 2005. "Predictability and model selection in the context of ARCH models," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 21(1), pages 55-82, January.
    10. Degiannakis, Stavros & Xekalaki, Evdokia, 2007. "Assessing the Performance of a Prediction Error Criterion Model Selection Algorithm in the Context of ARCH Models," MPRA Paper 96324, University Library of Munich, Germany.
    11. 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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    More about this item

    Keywords

    ARCH models; Monte Carlo Simulation; One-step-ahead Prediction Errors; Predictability; Standardized Prediction Error Criterion;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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