Copulas for Streaming Data

05/14/2018

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by   Alastair Gregory, et al.

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Empirical copula functions can be used to model the dependence structure of multivariate data. This paper adapts the Greenwald and Khanna algorithm in order to provide a space-memory efficient approximation to the empirical copula function of a bivariate stream of data. A succinct space-memory efficient summary of values seen in the stream up to a certain time is maintained and can be queried at any point to return an approximation to the empirical copula function with guaranteed error bounds. This paper then gives an example of a class of higher dimensional copulas that can be computed from a product of these bivariate copula approximations. The computational benefits and the approximation error of this algorithm is theoretically and numerically assessed.