Space-efficient estimation of empirical tail dependence coefficients for bivariate data streams

Abstract

This article proposes a space-efficient approximation to empirical tail dependence coefficients of an indefinite bivariate stream of data. The approximation, which has stream-length invariant error bounds, utilises recent work on the development of a summary for bivariate empirical copula functions. The work in this paper accurately approximates a bivariate empirical copula in the tails of each marginal distribution, therefore modelling the tail dependence between the two variables observed in the data stream. Copulas evaluated at these marginal tails can be used to estimate the tail dependence coefficients. Modifications to the space-efficient bivariate copula approximation, presented in this paper, allow the error of approximations to the tail dependence coefficients to remain stream-length invariant. Theoretical and numerical evidence of this, including a case-study using the Los Alamos National Laboratory netflow data-set, is provided within this article.