Time series analysis based on running Mann-Whitney Z Statistics
Article first published online: 22 AUG 2010
Published 2010. This article is a US Government work and is in the public domain in the USA.
Journal of Time Series Analysis
Volume 32, Issue 1, pages 47–53, January 2011
How to Cite
Mauget, S. (2011), Time series analysis based on running Mann-Whitney Z Statistics. Journal of Time Series Analysis, 32: 47–53. doi: 10.1111/j.1467-9892.2010.00683.x
- Issue published online: 12 DEC 2010
- Article first published online: 22 AUG 2010
- First version received November 2009 Published online in Wiley Online Library: 22 August 2010
- Mann–Whitney U statistics;
- moving window method;
- ranking based analysis;
- non-parametric statistics
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.