HARCH Processes are Heavy Tailed

Abstract

Heterogeneous Auto-Regressive Conditional Heteroskedastic processes were introduced by Mu ller, Dacarogna, Dave , Olsen, Pictet and von Weizsa cker in order to improve traditional ARCH-type models describing financial time series. In a later paper Embrechts, Samorodnitsky, Dacorogna and Mu ller asked how heavy the tails of stationary processes of this type are. We provide a partial answer to this question, using mainly monotonicity arguments to compare HARCH processes to other processes with a simpler recursive structure. [PUBLICATION ABSTRACT]