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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.

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Bibliographic Info

Paper provided by EconWPA in its series Econometrics with number 0411015.

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Length: 49 pages
Date of creation: 22 Nov 2004
Date of revision:
Handle: RePEc:wpa:wuwpem:0411015

Note: Type of Document - pdf; pages: 49
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Web page: http://128.118.178.162

Related research

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

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References

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  1. 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.
  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. 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.
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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. Amélie Charles, 2008. "Forecasting volatility with outliers in GARCH models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 27(7), pages 551-565.
  3. 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.
  4. David Neto & Sylvain Sardy & Paul Tseng, 2009. "l1-Penalized Likelihood Smoothing of Volatility Processes allowing for Abrupt Changes," Research Papers by the Department of Economics, University of Geneva 2009.05, Département des Sciences Économiques, Université de Genève.
  5. Jörg Polzehl & Vladimir Spokoiny & Catalin Starica, 2006. "When did the 2001 recession really start?," SFB 649 Discussion Papers SFB649DP2006-032, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  6. 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.

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