Time Series of Extremes

Abstract Data collected for the purpose of an extreme value analysis very often exhibit temporal dependence. Examples include daily time series of stock prices, temperature, or water levels. In this chapter, we address two fundamental inferential objectives: estimating extreme marginal quantiles while accounting for serial dependence, and estimating the strength of serial dependence in extreme values. We review the literature for methods aimed at each of these objectives, including a survey of computational methods used for each approach. We illustrate the methods using an analysis of hourly wind gust speeds. R code to implement the methods is available online.