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

## TL;DR

This paper introduces a space-efficient method to approximate empirical tail dependence coefficients in bivariate data streams, maintaining error bounds regardless of stream length, with theoretical and practical validation.

## Contribution

It develops a novel, space-efficient approximation for bivariate empirical copulas that accurately models tail dependence with stream-length invariant error bounds.

## Key findings

- Accurately approximates tail dependence in data streams
- Error bounds remain invariant with stream length
- Validated with real-world netflow data

## 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.