A Non-Parametric Approach to the Change-Point Problem
01 Jun 1979-Journal of The Royal Statistical Society Series C-applied Statistics (John Wiley & Sons, Ltd)-Vol. 28, Iss: 2, pp 126-135
TL;DR: In this paper, nonparametric techniques are introduced for the change point problem and exact and approximate results are obtained for testing the null hypothesis of no change for zero-one observations, Binomial observations, and continuous observations.
Abstract: Non‐parametric techniques are introduced for the change‐point problem. Exact and approximate results are obtained for testing the null hypothesis of no change. The methods are illustrated by the analysis of three sets of data illustrating the techniques for zero–one observations, Binomial observations and continuous observations. Some comparisons are made with methods based on cusums.
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TL;DR: In this paper, the European Climate Assessment (ECA) dataset was used to evaluate the daily European station series (1901-99) of surface air temperature and precipitation from the ECA dataset with respect to homogeneity.
Abstract: Daily European station series (1901–99) of surface air temperature and precipitation from the European Climate Assessment dataset are statistically tested with respect to homogeneity. A two-step approach is followed. First, four homogeneity tests are applied to evaluate the daily series. The testing variables used are (1) the annual mean of the diurnal temperature range, (2) the annual mean of the absolute day-to-day differences of the diurnal temperature range and (3) the wet day count (threshold 1 mm). Second, the results of the different tests are condensed into three classes: ‘useful’, ‘doubtful’ and ‘suspect’. A qualitative interpretation of this classification is given, as well as recommendations for the use of these labelled series in trend analysis and variability analysis of weather extremes. In the period 1901–99, 94% of the temperature series and 25% of the precipitation series are labelled ‘doubtful’ or ‘suspect’. In the sub-period 1946–99, 61% of the temperature series and 13% of the precipitation series are assigned to these classes. The seemingly favourable scores for precipitation can be attributed to the high standard deviation of the testing variable, and hence the inherent restricted possibilities for detecting inhomogeneities. About 65% of the statistically detected inhomogeneities in the temperature series labelled ‘doubtful’ or ‘suspect’ in the period 1946–99 can be attributed to observational changes that are documented in the metadata. For precipitation this percentage is 90%. Copyright 2003 Royal Meteorological Society.
747 citations
Cites background or methods from "A Non-Parametric Approach to the Ch..."
...If a break occurs in year E, then the statistic is maximal or minimal near the year k = E: XE = max 1≤k≤n |Xk| The significance level is given by Pettitt (1979)....
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...…test methods selected to test the departure of homogeneity in the time series are: the standard normal homogeneity test (SNHT) for a single break (Alexandersson, 1986), the Buishand range test (Buishand, 1982), the Pettitt test (Pettitt, 1979), and the Von Neumann ratio test (Von Neumann, 1941)....
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TL;DR: It is shown that the common trend TPR and Sawa’s Bayes criteria procedures seem optimal for most climate time series, whereas the SNH procedure and its nonparametric variant are probably best for mostClimate time series.
Abstract: This review article enumerates, categorizes, and compares many of the methods that have been proposed to detect undocumented changepoints in climate data series. The methods examined include the standard normal homogeneity (SNH) test, Wilcoxon’s nonparametric test, two-phase regression (TPR) procedures, inhomogeneity tests, information criteria procedures, and various variants thereof. All of these methods have been proposed in the climate literature to detect undocumented changepoints, but heretofore there has been little formal comparison of the techniques on either real or simulated climate series. This study seeks to unify the topic, showing clearly the fundamental differences among the assumptions made by each procedure and providing guidelines for which procedures work best in different situations. It is shown that the common trend TPR and Sawa’s Bayes criteria procedures seem optimal for most climate time series, whereas the SNH procedure and its nonparametric variant are probably best whe...
562 citations
01 Jan 2004
TL;DR: In this paper, general guidance is offered as to the methodology of change detection in time series of hydrological data, embracing stages such as preparing a suitable data set, exploratory analysis, application of adequate statistical tests and interpretation of results.
Abstract: General guidance is offered as to the methodology of change detection in time series of hydrological data, embracing stages such as preparing a suitable data set, exploratory analysis, application of adequate statistical tests and interpretation of results. Although the paper cannot go into full details of the many existing tests, it gives an easy-to-follow overview, offering practical hints and describing caveats and misconceptions. It serves as a refresher, raising attention to essential things that have often been ignored. A particular recommendation of the paper is that greater use of distribution-free testing methods, particularly resampling methods, should be made. These methods are recommended because they are particularly suited to hydrological data, which are often strongly skewed (non-normal), seasonal and serially correlated. Resampling techniques are flexible, robust and powerful, and require only minimal assumptions to be made about the data.
522 citations
TL;DR: Altman et al. as discussed by the authors showed that the asymptotic distribution of a re-scaled rank statistic is the same as the distribution of the Brownian bridge, which can be used to estimate the cutoff value of the continuous variable age.
489 citations
TL;DR: General guidance is offered as to the methodology of change detection in time series of hydrological data, embracing stages such as preparing a suitable data set, exploratory analysis, application of adequate statistical tests and interpretation of results.
Abstract: General guidance is offered as to the methodology of change detection in time series of hydrological data, embracing stages such as preparing a suitable data set, exploratory analysis, application of adequate statistical tests and interpretation of results. Although the paper cannot go into full details of the many existing tests, it gives an easy-to-follow overview, offering practical hints and describing caveats and misconceptions. It serves as a refresher, raising attention to essential things that have often been ignored. A particular recommendation of the paper is that greater use of distribution-free testing methods, particularly resampling methods, should be made. These methods are recommended because they are particularly suited to hydrological data, which are often strongly skewed (non-normal), seasonal and serially correlated. Resampling techniques are flexible, robust and powerful, and require only minimal assumptions to be made about the data.
482 citations