Small Sample Properties of GARCH Estimates and Persistence
AbstractIt is shown that the ML estimates of the popular GARCH(1,1) model are significantly negatively biased in small samples and that in many cases converged estimates are not possible with Bollerslev's non-negativity conditions. Results also indicate that a high level of persistence in GARCH(1,1) models obtained using a large number of observations has autocorrelations lower than these ML estimates suggest in small samples. Considering the size of biases and convergence errors, it is proposed that at least 250 observations are needed for ARCH(1) models and 500 observations for GARCH(1,1) models. A simple measure of how much GARCH conditional volatility explains squared returns is proposed. The measure indicates that for a typical index return volatility whose ARCH parameter is very small, the conditional volatility hardly explains squared returns.
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Bibliographic InfoPaper provided by Finance Lab, Insper Instituto de Ensino e Pesquisa in its series Finance Lab Working Papers with number flwp_48.
Date of creation: Oct 2003
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Other versions of this item:
- Soosung Hwang & Pedro L. Valls Pereira, 2006. "Small sample properties of GARCH estimates and persistence," European Journal of Finance, Taylor and Francis Journals, vol. 12(6-7), pages 473-494.
- NEP-ALL-2003-01-12 (All new papers)
- NEP-ECM-2003-01-12 (Econometrics)
- NEP-ETS-2003-01-12 (Econometric Time Series)
- NEP-RMG-2003-01-12 (Risk Management)
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