Working Paper

Regular Variation of Popular GARCH Processes Allowing for Distributional Asymmetry

Abstract: Linear GARCH(1,1) and threshold GARCH(1,1) processes are established as regularly varying, meaning their heavy tails are Pareto like, under conditions that allow the innovations from the, respective, processes to be skewed. Skewness is considered a stylized fact for many financial returns assumed to follow GARCH-type processes. The result in this note aids in establishing the asymptotic properties of certain GARCH estimators proposed in the literature.

Keywords: GARCH; Pareto tail; Heavy tail; Regular variation; Threshold GARCH;

JEL Classification: C20; C22; C53; C58;

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Bibliographic Information

Provider: Board of Governors of the Federal Reserve System (U.S.)

Part of Series: Finance and Economics Discussion Series

Publication Date: 2017-09-22

Number: 2017-095

Pages: 10 pages