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Varying coefficient GARCH versus local constant volatility modeling. Comparison of the predictive power


  • Jörg Polzehl
  • Vladimir Spokoiny


GARCH models are widely used in financial econometrics. However, we show by mean of a simple simulation example that the GARCH approach may lead to a serious model misspecification if the assumption of stationarity is violated. In particular, the well known integrated GARCH effect can be explained by nonstationarity of the time series. We then introduce a more general class of GARCH models with time varying coefficients and present an adaptive procedure which can estimate the GARCH coefficients as a function of time. We also discuss a simpler semiparametric model in which the beta-parameter is fixed. Finally we compare the performance of the parametric, time varying nonparametric and semiparametric GARCH(1,1) models and the locally constant model from Polzehl and Spokoiny (2002) by means of simulated and real data sets using different forecasting criteria. Our results indicate that the simple locally constant model outperforms the other models in almost all cases. The GARCH(1,1) model also demonstrates a relatively good forecasting performance as far as the short term forecasting horizon is considered. However, its application to long term forecasting seems questionable because of possible misspecification of the model parameters.

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  • Jörg Polzehl & Vladimir Spokoiny, 2006. "Varying coefficient GARCH versus local constant volatility modeling. Comparison of the predictive power," SFB 649 Discussion Papers SFB649DP2006-033, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  • Handle: RePEc:hum:wpaper:sfb649dp2006-033

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    References listed on IDEAS

    1. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
    2. Cătălin Stărică & Clive Granger, 2005. "Nonstationarities in Stock Returns," The Review of Economics and Statistics, MIT Press, vol. 87(3), pages 503-522, August.
    3. Liang Peng, 2003. "Least absolute deviations estimation for ARCH and GARCH models," Biometrika, Biometrika Trust, vol. 90(4), pages 967-975, December.
    4. Engle, Robert F & Sheppard, Kevin K, 2001. "Theoretical and Empirical Properties of Dynamic Conditional Correlation Multivariate GARCH," University of California at San Diego, Economics Working Paper Series qt5s2218dp, Department of Economics, UC San Diego.
    5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    6. Jianqing Fan & Juan Gu, 2003. "Semiparametric estimation of Value at Risk," Econometrics Journal, Royal Economic Society, vol. 6(2), pages 261-290, December.
    7. Giraitis, Liudas & Robinson, Peter M., 2001. "Whittle Estimation Of Arch Models," Econometric Theory, Cambridge University Press, vol. 17(03), pages 608-631, June.
    8. Thomas Mikosch & Catalin Starica, 2004. "Non-stationarities in financial time series, the long range dependence and the IGARCH effects," Econometrics 0412005, EconWPA.
    9. Berkes, Istv n & Horv th, Lajos & Kokoszka, Piotr, 2003. "Estimation Of The Maximal Moment Exponent Of A Garch(1,1) Sequence," Econometric Theory, Cambridge University Press, vol. 19(04), pages 565-586, August.
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    Cited by:

    1. Nazim Regnard & Jean-Michel Zakoïan, 2010. "Structure and estimation of a class of nonstationary yet nonexplosive GARCH models," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(5), pages 348-364, September.
    2. Xu, Ke-Li & Phillips, Peter C.B., 2008. "Adaptive estimation of autoregressive models with time-varying variances," Journal of Econometrics, Elsevier, vol. 142(1), pages 265-280, January.

    More about this item


    varying coefficient GARCH; adaptive weights;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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