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Deciding between GARCH and stochastic volatility via strong decision rules

  • PREMINGER, Arie
  • HAFNER, Christian M.

The GARCH and stochastic volatility (SV) models are two competing, well-known and often used models to explain the volatility of ï¬nancial series. In this paper, we consider a closed form estimator for a stochastic volatility model and derive its asymptotic properties. We conï¬rm our theoretical results by a simulation study. In addition, we propose a set of simple, strongly consistent decision rules to compare the ability of the GARCH and the SV model to ï¬t the characteristic features observed in high frequency ï¬nancial data such as high kurtosis and slowly decaying autocorrelation function of the squared observations. These rules are based on a number of moment conditions that is allowed to increase with sample size. We show that our selection procedure leads to choosing the best and simple model with probability one as the sample size increases. The ï¬nite sample size behaviour of our procedure is analyzed via simulations. Finally, we provide an application to stocks in the Dow Jones industrial average index.

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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2006042.

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Date of creation: 00 May 2006
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Handle: RePEc:cor:louvco:2006042
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