A Method to Quantify the Uncertainty in Copula Parameters When Studying Dependence Structures of Time Series

Analysis of existing data is the first step in preparing for human modification of natural water systems or existing water infrastructure. Time series of environmental measurements form an important part of that data. Such an analysis has as its aim the determination of the future operating conditions of the modified system. The dependence between time series is important both for normal operation and for the evaluation of risks in extreme situations. One way to study this dependence is through the use of copulas. But because the analysis is statistical in nature, its results, in this case the copula parameters, contain a certain amount of uncertainty. In this paper we demonstrate an approach that can be used to represent that uncertainty in cases where the dependence is modeled by a copula. The method is based on the confidence curve concept, that is it provides confidence sets for the parameter at all confidence levels. The use of confidence curves for copula parameters is a recent development. The confidence curve construction method uses a pseudo likelihood to avoid having to fit marginals to the data. This pseudo likelihood is then used to construct a confidence curve. The method was applied to annual maximum river discharge data for different tributaries of the Rhine to see how these are correlated.