  Empirical copula functions can be used to model the dependence structure of
multivariate data. The Greenwald and Khanna algorithm is adapted 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 bivariate copula
function with guaranteed error bounds. An example then illustrates how these
summaries can be used as a tool to compute approximations to higher dimensional
copula decompositions containing bivariate copulas. The computational benefits
and approximation error of the algorithm is theoretically and numerically
assessed.
