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Time series analysis based on running Mann-Whitney Z Statistics


Steve Mauget, U.S. Department of Agriculture-Agricultural Research Service, USDA Plant Stress and Water Conservation Laboratory, Lubbock, Texas, 3810 4th Street, Lubbock, Tx 79415, USA.


A time series analysis method based on the calculation of Mann–Whitney U statistics is described. This method samples data rankings over running time windows, converts those samples to Mann–Whitney U statistics, and then normalizes the U statistics to Z statistics using Monte-Carlo generated null parameters. Based on the Z statistics’ magnitudes this algorithm can identify time windows containing significant incidences of low or high data rankings, where the window length is determined by the sample size. By repeating this process with sampling windows of varying duration ranking regimes of arbitrary onset and duration can be objectively identified in a time series. The simplicity of the procedure's output – a time series’ most significant non-overlapping ranking sequences – makes it possible to graphically identify common temporal breakpoints and patterns of variability in the analyses of multiple time series. This approach is demonstrated using United States annual temperature data during 1896–2008.