Time Series Analysis Based on Running Mann Whitney Z Statistics

Authors: Mauget, Steven

Submitted to: Trade Journal Publication
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 6/9/2010
Publication Date: 1/1/2011
Citation: Mauget, S.A. 2011. Time Series Analysis Based on Running Mann Whitney Z Statistics. Journal of Time Series Analysis. 32(1): 47-53.

Interpretive Summary: Because most methods of time series analysis make limiting assumptions about how data varies in time, those methods are not able to detect the ways that data really varies. For example, the cyclic, random, and intermittent ways that long-term climate time series tend to behave. To detect the more arbitrary ways that natural data varies, a new time series analysis method based on the calculation of Mann Whitney U statistics is proposed and described via an analysis of U.S. temperature data during 1896-2008. This method samples data rankings over moving time windows, converts those samples to Mann-Whitney U statistics, and then normalizes the U statistics to Z statistics that can be tested for statistical significance. This method can detect a wide range of data variation because it makes relatively few limiting assumptions about how data varies over time. The basic assumption is that time series might contain significant ranking regimes, but a wide range of data variability can be expressed in terms of such regimes. For example, a gradual increase in temperature during 19896-2008 might be marked by low temperature rankings at the time series’ beginning, and significant high rank periods at the end. Intermittent cyclic regimes might result in alternating high and low ranked periods. Thus by detecting what might be considered a basic ‘building block’ of data variation over time, i.e., ranking regimes of arbitrary onset and duration, the method can detect arbitrary patterns of data variability within a time series. This method is also objective in that it can identify runs of extreme rankings, but imposes no arbitrary thresholds that define extreme rankings. The simplicity of the method’s results allows for the graphic comparison of the analysis of many time series, and the identification of common periods of high and low rankings.

Technical Abstract: A sensitive and objective time series analysis method based on the calculation of Mann Whitney U statistics is described. This method samples data rankings over moving 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 process can identify time windows containing significant incidences of low or high rankings, where the window length is determined by the sample size. By repeating this process with sampling windows of varying duration, the method can objectively identify ranking regimes of arbitrary onset and duration in a time series. The simplicity of the method’s output – a time series’ most significant non-overlapping ranking regimes – makes it possible to graphically identify common temporal breakpoints and patterns of variability in the analyses of multiple time series. The method is demonstrated using United States annual temperature data during 1896-2008.