A Practical Guide for Detecting Abrupt Changes in Time Series
Aiguo Dai, NCAR, Boulder, CO
Abrupt changes in climate and other time series often arise due to physical or measurement changes, and it is often desirable to detect and separate such rapid changes in data analyses. Many statistical methods have been developed for detecting these changes, but their performance has been shown to vary considerably. Through carefully designed numerical experiments with several representative types of change functions added to a random Gaussian process, we quantitatively compare four types of widely-used detection methods in terms of their detection rate and error. It is found that for stepwise changes with small trends, the multi-response permutation procedure (MRPP) performs best with the smallest failure rate and error, closely followed by the simple Student-t test for difference in the mean. The two-phase regression model (TPRM) and the Mann-Kendall rank sum (MKRS) test perform considerably worse for stepwise changes. The existence of secondary changes or small trends could either improve the detection results when they are in a direction to enlarge the primary change or deteriorate the results when they reduce the primary change. For changes in trends or stepwise changes with large trends, however, only the TPRM method works well. It is found that using the F3,N-4 distribution for the TPRM method leads to slightly larger detection errors but considerably higher detection rates than using the Fmax,0.90 percentiles of Lund and Reeves (2002). Our results can be used to alleviate the dilemma faced by any detection method to be able to detect small changes but not false ones by comparing the size of the detected change to the s.d. of the residual time series. When the size of the change D is large relative to the s.d. (e.g., D>1 s.d.), the MRPP and Student-t test can capture most (>95%) of the stepwise changes with most (>90%) of them close to the prescribed change point (i.e., not false detection of random points). For trend-type changes, the contrast in the slopes is also important for the TPRM.
Applications to four time series from the real world show that multiple abrupt change points can be successfully detected using these methods. The detected abrupt changes include a jump around 1945 and a drop around 1972 in June peak streamflow in the Columbia River; a drop around March 1944 and a jump around June 1976 in the Pacific Decadal Oscillation index; a change in the global warming rates during different periods: 1850-1901, 1902-1945, 1946-1976, and 1977-2007; and abrupt rises in atmospheric CO2 concentrations around 423.4, 332.4, 241.4, and 132.4 thousand years before present in ice-core records. Based on the results, a practical guide to detect abrupt changes in time series is suggested.
Session 9B, Observed changes in climate - II
Wednesday, 14 January 2009, 10:30 AM-12:00 PM, Room 129B
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