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Is GARCH(1,1) as good a model as the Nobel prize accolades would imply?

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  • Catalin Starica

    (Chalmers University of Technology, Göteborg, Sweden)

Abstract

This paper investigates the relevance of the stationary, conditional, parametric ARCH modeling paradigm as embodied by the GARCH(1,1) process to describing and forecasting the dynamics of returns of the Standard & Poors 500 (S&P 500) stock market index. A detailed analysis of the series of S&P 500 returns featured in Section 3.2 of the Advanced Information note on the Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel reveals that during the period under discussion, there were no (statistically significant) differences between GARCH(1,1) modeling and a simple non-stationary, non-parametric regression approach to next-day volatility forecasting. A second finding is that the GARCH(1,1) model severely over-estimated the unconditional variance of returns during the period under study. For example, the annualized implied GARCH(1,1) unconditional standard deviation of the sample is 35% while the sample standard deviation estimate is a mere 19%. Over-estimation of the unconditional variance leads to poor volatility forecasts during the period under discussion with the MSE of GARCH(1,1) 1-year ahead volatility more than 4 times bigger than the MSE of a forecast based on historical volatility. We test and reject the hypothesis that a GARCH(1,1) process is the true data generating process of the longer sample of returns of the S&P 500 stock market index between March 4, 1957 and October 9, 2003. We investigate then the alternative use of the GARCH(1,1) process as a local, stationary approximation of the data and find that the GARCH(1,1) model fails during significantly long periods to provide a good local description to the time series of returns on the S&P 500 and Dow Jones Industrial Average indexes. Since the estimated coefficients of the GARCH model change significantly through time, it is not clear how the GARCH(1,1) model can be used for volatility forecasting over longer horizons. A comparison between the GARCH(1,1) volatility forecasts and a simple approach based on historical volatility questions the relevance of the GARCH(1,1) dynamics for longer horizon volatility forecasting for both the S&P 500 and Dow Jones Industrial Average indexes.

Suggested Citation

  • Catalin Starica, 2004. "Is GARCH(1,1) as good a model as the Nobel prize accolades would imply?," Econometrics 0411015, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpem:0411015
    Note: Type of Document - pdf; pages: 49
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/em/papers/0411/0411015.pdf
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    References listed on IDEAS

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    1. French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, vol. 19(1), pages 3-29, September.
    2. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    3. I. Gijbels & A. Pope & M. P. Wand, 1999. "Understanding exponential smoothing via kernel regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 39-50.
    4. Merton, Robert C., 1980. "On estimating the expected return on the market : An exploratory investigation," Journal of Financial Economics, Elsevier, vol. 8(4), pages 323-361, December.
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    Citations

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    Cited by:

    1. Gürtler, Marc & Rauh, Ronald, 2012. "Challenging traditional risk models by a non-stationary approach with nonparametric heteroscedasticity," Working Papers IF41V1, Technische Universität Braunschweig, Institute of Finance.
    2. Hafner, Christian M. & Linton, Oliver, 2010. "Efficient estimation of a multivariate multiplicative volatility model," Journal of Econometrics, Elsevier, vol. 159(1), pages 55-73, November.
    3. Gürtler, Marc & Rauh, Ronald, 2009. "Shortcomings of a parametric VaR approach and nonparametric improvements based on a non-stationary return series model," Working Papers IF32V2, Technische Universität Braunschweig, Institute of Finance.
    4. J. Polzehl & V. Spokoiny & C. Starica, 2004. "When did the 2001 recession really start?," Econometrics 0411017, University Library of Munich, Germany.
    5. David Neto & Sylvain Sardy & Paul Tseng, 2009. "l1-Penalized Likelihood Smoothing of Volatility Processes allowing for Abrupt Changes," Research Papers by the Institute of Economics and Econometrics, Geneva School of Economics and Management, University of Geneva 2009.05, Institut d'Economie et Econométrie, Université de Genève.
    6. Gürtler, Marc & Kreiss, Jens-Peter & Rauh, Ronald, 2009. "A non-stationary approach for financial returns with nonparametric heteroscedasticity," Working Papers IF31V2, Technische Universität Braunschweig, Institute of Finance.
    7. Amélie Charles, 2008. "Forecasting volatility with outliers in GARCH models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 27(7), pages 551-565.
    8. Claudio Bonilla & Jean Sepulveda, 2011. "Stock returns in emerging markets and the use of GARCH models," Applied Economics Letters, Taylor & Francis Journals, vol. 18(14), pages 1321-1325.

    More about this item

    Keywords

    stock returns; volatility; Garch(1; 1); non-stationarities; unconditional time-varying volatility; IGARCH effect; longer-horizon forecasts;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • 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

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