Lori Thombs
Department of Statistics
University of South Carolina
Resampling Techniques for GARCH Modeling
In this paper, we study the problem of model identification for GARCH
models. Such models, first introduced by Engle (1982), allow for
time-varying behavior of the variance. A general approach to fitting
such models is to exploit the similarity between the correlation
structure of the squares of the GARCH(p,q) series and that of a
traditional stationary and invertible ARMA model. However, in this
ARMA representation for the squares of the GARCH data, the innovations
are serially uncorrelated, but not independent, over time. The
importance of distinguishing between mere uncorrelated variates and
independence was illustrated by Thombs and Romano (1996), who show
that standard inferential methods for the estimated autocorrelations
can be misleading in such a setting. We propose use the moving block
bootstrap for inference about both the autocorrelation and partial
autocorrelation function of the squared GARCH data. Interval
estimation using the bias corrected percentile interval is also shown
to outperform the standard method.
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