Detection of Undocumented Changepoints: A Revision of the Two-Phase Regression Model

Abstract

Changepoints (inhomogeneities) are present in many climatic time series. Changepoints are physically plausible whenever a station location is moved, a recording instrument is changed, a new method of data collection is employed, an observer changes, etc. If the time of the changepoint is known, it is usually a straightforward task to adjust the series for the inhomogeneity. However, an undocumented changepoint time greatly complicates the analysis. This paper examines detection and adjustment of climatic series for undocumented changepoint times, primarily from single site data. The two-phase regression model techniques currently used are demonstrated to be biased toward the conclusion of an excessive number of unobserved changepoint times. A simple and easily applicable revision of this statistical method is introduced.

Changes in temperature extremes over Italy in the last 44 years

“…The first step in the analysis of our time series is the identification of possible change points; since many techniques have been applied in previous studies, we applied at first the Mann-Kendall progressive series (Sneyers, 1990) and looked for a confirmation of a change point with two tests: the 'two-phase regression' (TPR) parametric test, revised by Lund and Reeves (2002), and, when a period of stationarity followed by a trend seemed plausible, the Standard Normal Homogeneity Test (SNHT) in trend version (Alexandersson and Moberg, 1997); in both cases we chose a p-value of 0.05. In the application of the Mann-Kendall progressive series, as explained by Sneyers and Escudero (2000), a no-trend hypothesis is confirmed if the progressive series remains near zero, while if the series diverges systematically from zero after a certain point, this can be considered as a first determination of a change point; therefore, in applying this method we followed a visual approach in identifying the change point.…”

“…The statistic is computed for each year and if the maximum of the statistic, F max , overcomes the value (which is a function of the significance level and the number of data) of the F max distribution under the null hypothesis, the year is classified as a change point. The percentiles of the F max distribution were calculated via simulation by Lund and Reeves (2002), in order to resolve the overestimation caused by the use of the F 3,n−4 (where n is the number of data) to approximate the real distribution (for example, Solow, 1987;Easterling and Peterson, 1995). The SNHT-trend version is based on the likelihood ratio constructed on the null hypothesis of stationarity versus the alternative one that allows for a trend starting in a determined year; as in the case of TPR test, if the statistic in a year overcomes a specific value (Alexandersson and Moberg, 1997 for details and a table of values) the year is considered a change point.…”

Exact and efficient Bayesian inference for multiple changepoint problems

“…Some examples include Poisson processes with a piece-wise constant rate parameter (Raftery and Akman, 1986;Yang and Kuo, 2001;Ritov et al, 2002), changing linear regression models (Carlin et al, 1992;Lund and Reeves, 2002), Gaussian observations with varying mean (Worsley, 1979) or variance (Chen and Gupta, 1997;Johnson et al, 2003), and Markov models with time-varying transition matrices (Braun and Muller, 1998). Such models have been used for modelling stock prices, muscle activation, climatic time-series, DNA sequences and neuronal activity in the brain, amongst many other applications…”

Segmented regression, a versatile tool to analyze mRNA levels in relation to DNA copy number aberrations

“…However, if the change-point(s) has to be estimated from the data, the test statistics no longer follow an F-distribution under the null hypothesis, and the P-values have to be based on the bootstrapped (Hinkley, 1988) or simulated distribution of the test statistics (Julious, 2001;Lund and Reeves, 2002), or on permutations (Kim et al, 2000). Because of computational constraints, we chose to simulate the distribution for the F-statistics.…”