Testing for a Unit Root in a Time Series With a Changing Mean: Corrections and Extensions

This article explores the relation between nonexponential waiting times between events and the distribution of the number of events in a fixed time interval. It is shown that within this framework the frequently observed phenomenon of overdispersion—that is, a variance that exceeds the mean—is caused by a decreasing hazard function of the waiting times, whereas an increasing hazard function leads to underdispersion. Using the assumption of iid gamma-distributed waiting times, a new count-data model is derived. Its use is illustrated in two applications, the number of births and the number of doctor consultations.     

Multivariate autoregressive extreme value process and its application for modeling the time series properties of the extreme daily asset prices

Abstract

In this article we suggest a new multivariate autoregressive process for modeling time-dependent extreme value distributed observations. The idea behind the approach is to transform the original observations to latent variables that are univariate normally distributed. Then the vector autoregressive DCC model is fitted to the multivariate latent process. The distributional properties of the suggested model are extensively studied. The process parameters are estimated by applying a two-stage estimation procedure. We derive a prediction interval for future values of the suggested process. The results are applied in an empirically study by modeling the behavior of extreme daily stock prices.