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Application of FIGARCH and EWMA Models on Stock Indices PX and BUX

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  • Zdeněk Štolc

Abstract

Volatility of the financial time series belongs to the crucial estimated parameters in finance (e.g. in risk management, derivative pricing). It is well known, that volatility varies in time, so that new approaches of volatility modeling have appeared. In this paper two models of the conditional heteroskedasticity - fractionally integrated GARCH (FIGARCH) and EWMA are presented. These models are illustrated on the daily historical returns of stock index PX and index BUX. Standard tests of normality, autocorrelation and conditional heteroskedasticity are applied to these log-return time series and before estimating the models, which confirm a usability of the conditional heteroskedasticity models. Empirical results of the Rescale Range analysis (R/S) indicate a long memory in the volatility process of PX index and the first 40 autocorrelations of the square log-returns show their hyperbolic decay. The volatility models are estimated by quasi-maximum likelihood method with Student´s t-distribution and used to the calculation of the 1-day 95% and 99% Value at Risk values. Finally, the validity of the models is verified by Kupiec´s test, TUFF and Christoffersen´s test. These tests demonstrate, that the FIGARCH model is a suitable alternative to the EWMA model in the Value at Risk calculation.

Suggested Citation

  • Zdeněk Štolc, 2011. "Application of FIGARCH and EWMA Models on Stock Indices PX and BUX," Acta Oeconomica Pragensia, University of Economics, Prague, vol. 2011(4), pages 25-38.
  • Handle: RePEc:prg:jnlaop:v:2011:y:2011:i:4:id:338:p:25-38
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    References listed on IDEAS

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    1. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
    2. Granger, C. W. J., 1980. "Long memory relationships and the aggregation of dynamic models," Journal of Econometrics, Elsevier, vol. 14(2), pages 227-238, October.
    3. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-862, November.
    4. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
    5. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters,in: THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78 World Scientific Publishing Co. Pte. Ltd..
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    More about this item

    Keywords

    Value at Risk; PX and BUX indices; fractionally integrated process; FIGARCH; EWMA;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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