Sub-sample Bootstrap Prediction Intervals in GARCH Models

Yun-Huan Lee
June 2011
European Journal of Social Sciences;Jun2011, Vol. 22 Issue 2, p188
Academic Journal
This paper proposes using a subsample bootstrap method to create a prediction interval in a GARCH model with heavy-tailed distribution. The subsample bootstrap method refers to a phenomenon in that the number of bootstrap samples is lower than the original number of samples taken during the sampling process and estimator variance could be increased. When the GARCH model had heavy-tailed distribution, Hall and Yao (2003) were able to obtain consistent estimation of parametric values for sample distribution, by using this method. This sampling process used the quasi-maximum likelihood method to estimate the parameters for the validation of the prediction interval produced by the sub-sample bootstrap method. Simulation result indicated that when the ratio of the number of subsample bootstrap samples and those in traditional bootstrap methods was 0.7, the interval length and the coverage probability were the same as that of the traditional bootstrap method. When a prediction interval was determined through this method, without affecting the accuracy level, computation time was reduced.


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