Resampling Hypothesis Tests for Autocorrelated Fields

Presently employed hypothesis tests for multivariate geophysical data (e.g., climatic fields) require the assumption that either the data are serially uncorrelated, or spatially uncorrelated, or both. Good methods have been developed to deal with temporal correlation, but generalization of these methods to multivariate problems involving spatial correlation has been problematic, particularly when (as is often the case) sample sizes are small relative to the dimension of the data vectors. Spatial correlation has been handled successfully by resampling methods when the temporal correlation can be neglected, at least according to the null hypothesis. This paper describes the construction of resampling tests for differences of means that account simultaneously for temporal and spatial correlation. First, univariate tests are derived that respect temporal correlation in the data, using the relatively new concept of "moving blocks" bootstrap resampling. These tests perform accurately for small samples and are nearly as powerful as existing alternatives. Simultaneous application of these univariate resampling tests to elements of data vectors (or fields) yields a powerful (i.e., sensitive) multivariate test in which the cross correlation between elements of the data vectors is successfully captured by the resampling, rather than through explicit modeling and estimation.