The GJR GARCH(1,1) Process As Regularly Varying: Implications for Efficient Model Estimation and Risk Measurement

26 Pages Posted: 5 Aug 2017 Last revised: 13 Mar 2018

Multiple version iconThere are 2 versions of this paper

Date Written: March 9, 2018

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.

Keywords: GARCH, Threshold GARCH, Heavy Tail, Pareto Tail, Regular Variation, efficient method of moments

JEL Classification: C20, C22, C53, C58

Suggested Citation

Prono, Todd, The GJR GARCH(1,1) Process As Regularly Varying: Implications for Efficient Model Estimation and Risk Measurement (March 9, 2018). Available at SSRN: https://ssrn.com/abstract=3013353 or http://dx.doi.org/10.2139/ssrn.3013353

Todd Prono (Contact Author)

Federal Reserve Board ( email )

20th and Constitution Ave NW
Washington, DC 20551
United States

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