Is Garch(1,1) as Good a Model as the Accolades of the Nobel Prize Would Imply?

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 amp; Poors 500 (Samp;P 500) stock market index.A detailed analysis of the series of Samp;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 findingis 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 Samp;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 timeseries of returns on the Samp;P 500 and Dow Jones Industrial Average indexes.Since the estimated coeffcients 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 Samp;P 500 and Dow Jones Industrial Average indexes