A composite statistical method for the detection of multiple undocumented abrupt changes in the mean value within a time series

摘要

The time series of measurements of hydro-meteorological variables often suffer from imperfections such as missing data, outliers and discontinuities in the mean values. The discontinuity in the mean can be the effect of: instrumental offsets and of their corrections, of changes in the monitoring station or in the surrounding environment. If the discontinuities can be identified with a reasonable precision, a correction of the erroneous data can be made. Several authors have put their great effort into developing techniques to identify non-climatic inhomogeneities; the resulting statistical methods are especially effective when the series contains a single change point, while their performances decline when the series contains multiple change points or inhomogeneous segments (a portion of the series bounded by two complementary shifts). These limitations also affect the standard normal homogeneity test (SNHT), one of the most effective and widely applied tests. We present a composite method of homogeneity testing, standard normal homogenization composite method (SNHCM), including the SNHT as one component, which improves the SNHT performances with multiple change points and inhomogeneous segments. A number of comparisons among the new method, the SNHT and a powerful optimal segmentation method (OSM-CM), are illustrated in the paper. SNHCM demonstrates their performances in change-point detection similar to, or better than, the SNHT and very close to the OSM-CM. The SNHCM is effective in recognizing complex patterns of discontinuities, especially inhomogeneous segments, which represent a severe problem for SNHT; on the contrary, SNHT performs slightly better only when the series contains a single change point, but the difference between the two methods is negligible. Compared to the OSM-CM, SNHCM provides very similar performances, with some favourable features deriving from the fact that it is computationally lighter, simpler to implement, can easily handle very long series and is based on statistical hypothesis tests with a well-defined and adjustable significance level.