Scanning Detections of Multi-scale Significant Change-Points in Subseries Means, Variances, Trends and Correlations

This paper presents four detecting algorithms of multi-scale significant change points with both corrections of the dependence and of non-normal distribution in the series to be tested. The four algorithms are respectively the scanning t-test of changes in subseries means or averages (the first center moment), the scanning F-test of changes in subseries variances or standard deviations, the scanning F-test of changes in subseries trends or regressions to time, and the scanning U-test of changes in subseries correlation coefficients or co-variances for a pair time series (the second moment). Their common feature is of combining the classical statistics with the wavelet algorithm, and of giving statistic criteria at corresponding confidence as well as automatic and objective detection on various time scales. These algorithms also carried out coherency detections of significant changes in each of the four terms for a pair objects. In addition, a new scheme for normalizing data of non-normal probability distribution is described in a non-parameter technique - the quantile method.