Zhengjun Zhang
Professor
Department of Statistics
University of Wisconsin
Madison, Wisconsin
 

ATM: Autoregressive Tail-index Model for Financial Time Series

Abstract:  Classical generalized extreme value (GEV) model has been widely used in financial risk management. In this paper, we extend the static GEV modeling to dynamic modeling by introducing an autoregressive evolution scheme on the three parameters of GEV. Specifically, an autoregressive tail model (ATM) is proposed to better study tail behavior changes of time series. Probabilistic properties of the model is studied and an maximum likelihood estimator (MLE) is proposed for model estimation. Asymptotic properties of MLE is derived and finite sample performance is illustrated by simulations. To demonstrate the superior performance of dynamic GEV modeling, we apply the proposed modeling scheme to cross-sectional maxima of negative daily log-returns for components of S&P100 and to daily maxima of 3-minute negative log-returns for high frequency trading of foreign exchanges (JPY v.s. USD). This is a joint work with Zifeng Zhao and Rong Chen.

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