Comparisons of multivariate relational structures in serially correlated data

An approach for carrying out between-group comparisons of multivariate relationships in the presence of serially correlated data is presented, evaluated, and illustrated. The method has potential applications in many areas of environmental research and is demonstrated in the context of evaluating the performance of an atmospheric model used to predict measures of air quality and acid deposition. The multivariate relationships are initially characterized using principal component analysis. The comparison of subspaces defined by the principal component eigenvectors is investigated using four different test statistics, constructed in such a way as to facilitate the evaluation of discrete aspects of the methodology A test of the hypothesis of equal subspaces involves subjecting the data from one group to an orthogonal rotation so as to force coincidence of the subspaces, thereby replicating the null hypothesis. Statistical significance is assessed by applying a nonparametric blockwise bootstrap procedure to a series of vector observations. A simulation-based evaluation of the procedure suggests that a conservative test can be obtained in most cases for three of the four statistics. The performance of the fourth is more dependent upon sample size and the strength of data dependencies; however, in some cases it produced conservative results closer to the nominal level than the others.