Copula fitting to autocorrelated data, with applications to wind speed modelling

Abstract. Copulas became a popular tool in multivariate modelling, with several fitting methods readily available. In an earlier paper [19] we focused on the goodness of fit for copulas. These tests are based on independent samples. To assume complete independence for time series data is usually too optimistic. Now, as in real applications time dependence is a common feature, we turn to the investigation of the effect of this phenomenon to the proposed test-statistics, especially to the Kendall's process approach of [5] and [6]. The block bootstrap methodology is used for defining the effective sample size for time dependent bivariate observations. The critical values are then computed by simulation from independent samples with the adjusted size, determined by these bootstrap methods. The methods are illustrated by 2-dimensional modelling of the weekly maxima of 50-years observations of wind data for German sites. We also propose methods for assessing the reliability of the prediction regions, introduced in [18].