Abstract
Linear GARCH(1,1) and GJR GARCH(1,1) processes are established as regularly varying, meaning their heavy tails follow a Power Law, under conditions that allow the innovations from the, respective, processes to be either symmetrically distributed or skewed. Skewness is considered a stylized fact for many financial returns, as is the tendency of (high frequency) financial returns to display strong GARCH effects. A joint, exactly-identified method-of-moments estimator is proposed for the parameters of these GARCH processes that includes the tail index, and the asymptotic properties of this estimator are determined. Owing to it being efficient, this estimator compares (quite) favorably against competing two-step alternatives available in the literature.
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