Similarity‐based clustering for patterns of extreme values

Abstract

Statistical modelling of the magnitude and the frequency of extreme observations is fundamental for a variety of sciences. In this paper, we develop statistical methods of similarity‐based clustering for heteroscedastic extremes, which allow us to group time series of independent observations according to their extreme‐value index and scedasis function (i.e., the magnitude and frequency of extreme values, respectively). Clustering scedasis functions and extreme‐value indices involves the challenge of grouping objects composed of both a function (scedasis) and a scalar (extreme‐value index), and thus the need to partition a product‐space. Our analysis reveals an interesting mismatch between the magnitude and frequency of extreme losses on the London Stock Exchange and the corresponding economic sectors of the affected stocks. The analysis further suggests that the dynamics governing the comovement of extreme losses in the exchange contains information on the business cycle.