Statistical Inference for Heavy Tailed Time Series and Vectors

ISBN-13: 9783330035126 / Angielski / Miękka / 2017 / 220 str.

Zhigang Tong

Opis

In this book we deal with statistical inference related to extreme value phenomena. Specifically, if X is a random vector with values in d-dimensional space, our goal is to estimate moments of (X) for a suitably chosen function when the magnitude of X is big. We employ the powerful tool of regular variation for random variables, random vectors and time series to formally define the limiting quantities of interests and construct the estimators. We focus on three statistical estimation problems: (i) multivariate tail estimation for regularly varying random vectors, (ii) extremogram estimation for regularly varying time series, (iii) estimation of the expected shortfall given an extreme component under a conditional extreme value model. We establish asymptotic normality of estimators for each of the estimation problems. The theoretical findings are supported by simulation studies and the estimation procedures are applied to some financial data.

O autorze

Zhigang Tong received PhD degree in Mathematics from Department of Mathematics and Statistics in University of Ottawa, Canada. He is interested in applying multivariate regular variation and tail empirical processes to the statistical inference related to extreme value phenomena, with particular emphasis on applications to risk management.