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 ar e serially uncorrelated, or spatially uncorrelated, or both. Good meth ods have been developed to deal with temporal correlation, but general ization of these methods to multivariate problems involving spatial co rrelation has been problematic, particularly when (as is often the cas e) sample sizes are small relative to the dimension of the data vector s. Spatial correlation has been handled successfully by resampling met hods when the temporal correlation can be neglected, at least accordin g to the null hypothesis. This paper describes the construction of res ampling 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 n ew concept of ''moving blocks'' bootstrap resampling. These tests perf orm accurately for small samples and are nearly as powerful as existin g alternatives. Simultaneous application of these univariate resamplin g 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 resampli ng, rather than through explicit modeling and estimation.