Homogeneity testing for spatially correlated data in multivariate regional frequency analysis

Identification of homogeneous regions is a key task in regional frequency analysis (RFA) to obtain adequate quantile estimates for an event of interest. Recently, the frequently used univariate Hosking-Wallis L-moment homogeneity test was extended to the multivariate case. Multivariate L-moments are used as a tool to define the test statistic and copula models to describe the statistical behavior of the analyzed dependent variables. To avoid drawbacks in fitting a parametric joint distribution to the data and a rejection threshold which is based on simulations, its nonparametric alternatives were also proposed. Although the simulation studies performed demonstrated the usefulness of both the parametric and nonparametric tests, the powers obtained were valid only for regions without intersite dependence. Examples from practice nevertheless demonstrate that intersite correlation may be expected for some kinds of data. To overcome the problem of cross correlation between stations, the parametric testing procedure is generalized using D-vine copulas to model intersite dependence when generating synthetic homogeneous regions during the testing procedure. Monte Carlo simulations were performed and illustrate how intersite dependence negatively impacts the multivariate L-moment homogeneity tests by significantly reducing their powers. The results of simulations also demonstrate the superiority of the proposed modification over both the original parametric and nonparametric procedures inasmuch as it improves the heterogeneity detection and avoids miscategorization of a region. The modified test is also applied in a case study for meteorological data in the Czech Republic.