Modeling Maxima with Autoregressive Conditional Fr\'echet Model
报 告 人:: 张正军
报告地点:: 数学与统计学院四楼报告厅
报告时间:: 2017年12月21日星期四16:00-16:45

This talk introduces a novel dynamic generalized extreme value~(GEV) framework for modeling the time-varying behavior of maxima in financial time series. Specifically, an autoregressive conditional Fr\'echet~(AcF) model is proposed in which the maxima are modeled by a Fr\'echet distribution with time-varying scale parameter~(volatility) and shape parameter~(tail index) conditioned on past information. The AcF provides a direct and accurate modeling of the time-varying behavior of maxima and offers a new angle to study the tail risk dynamics in financial markets. Probabilistic properties of AcF are studied, and a maximum likelihood estimator is used for model estimation, with its statistical properties investigated. Simulations show the flexibility of AcF and confirm the reliability of its estimators. Two real data examples on cross-sectional stock returns and high-frequency foreign exchange returns are used to demonstrate the AcF modeling approach, where significant improvement over the static GEV has been observed for market tail risk monitoring and conditional VaR estimation. Empirical result of AcF is consistent with the findings of the dynamic peak-over-threshold~(POT) literature that the tail index of financial markets varies through time.

发 布 人:科研助理 发布时间: 2017-12-13
Professor of Statistics in the Department of Statistics at the University of Wisconsin. Main research contributions: max-linear econometrics in the big data with publications in Journal of Econometrics, Journal of Royal Statistical Society B, Journal of Banking and Finance, Advances in Econometrics, Journal of American Statistical Association, Annals of Statistics, Journal of Applied Probability, Insurance Mathematics and Economics.