Single Change Point Detection Research Articles

Changepoint detection with the use of the RESPERM method – a Monte Carlo study

RESPERM (residuals permutation-based method) is a single changepoint detection method based on regression residuals permutation, which can be applied to many physiological situations where the regression slope can change suddenly at a given point. This article presents the results of a Monte Carlo study on the properties of the RESPERM method for single changepoint detection in a linear regression model. We compared our method with a well-known segmented method for detection breakpoint in linear models. The Monte Carlo study showed that when the input data are very noisy, the RESPERM method outperforms the segmented approach in terms of variance, and in the case of bias, the results of the two methods are comparable.

Change-Point Detection in the Volatility of Conditional Heteroscedastic Autoregressive Nonlinear Models

This paper studies single change-point detection in the volatility of a class of parametric conditional heteroscedastic autoregressive nonlinear (CHARN) models. The conditional least-squares (CLS) estimators of the parameters are defined and are proved to be consistent. A Kolmogorov–Smirnov type-test for change-point detection is constructed and its null distribution is provided. An estimator of the change-point location is defined. Its consistency and its limiting distribution are studied in detail. A simulation experiment is carried out to assess the performance of the results, which are compared to recent results and applied to two sets of real data.

Detecting and testing multiple change points in distributions of damage-sensitive feature data for data-driven structural condition assessment: A distributional time series change-point analytic approach

Structural change detection is a core component of structural health monitoring (SHM). One appealing aspect of SHM is that structural changes can be detected by detecting the changes in extracted damage-sensitive features (DSFs). The feature changes of the data are usually attributed to the changes of the underlying distributions; thus, developing reliable change-point detectors for automatically detecting and testing various potential changes in the distributions of DSF data are particularly beneficial for automatic structural health diagnosis. However, methodological researches devoted to detecting change points for probability distributions are rare either in statistics or engineering literature, and state-of-the-art approaches mainly focus on single change-point detection and have restrictive assumptions on the distributions or the types of change points. This motivates us to develop a more flexible multiple change-point detection method for the distributions of DSF data employed for data-driven structural condition assessment. To accommodate a large dataset, the DSF data are summarized by a distributional time series that consists of probability density functions (PDFs) estimated from blocks of DSF data. Then, detecting the distributional changes for the massive DSF data can be phrased as detecting the changes in the resulting distributional time series with much less data objects. To overcome the obstacle that the PDF-valued data are special functional data residing in nonlinear abstract spaces, this study employs two transformations to convert the PDFs into more tractable vector spaces. Then, by using the linear structures possessed by the vector spaces, a nonparametric multiple change-point detection method is presented for the distributional time series based on the techniques of functional principal component analysis and E-Divisive data segmentation. The proposed method possesses various nice features, such as being capable for multiple change-point detection, having fewer restrictive assumptions and scalability to large datasets. Moreover, it also shows superiority in revealing the modes of distributional variations. An application to distributional change detection involved in cable condition assessment for a long-span cable-stayed bridge demonstrates the applicability and versatility of our proposal, and some interesting results are also discovered.

A Weighted Error Distance Metrics (WEDM) for Performance Evaluation on Multiple Change-Point (MCP) Detection in Synthetic Time Series.

Change-point detection (CPD) is to find abrupt changes in time-series data. Various computational algorithms have been developed for CPD applications. To compare the different CPD models, many performance metrics have been introduced to evaluate the algorithms. Each of the previous evaluation methods measures the different aspects of the methods. Based on the existing weighted error distance (WED) method on single change-point (CP) detection, a novel WED metrics (WEDM) was proposed to evaluate the overall performance of a CPD model across not only repetitive tests on single CP detection, but also successive tests on multiple change-point (MCP) detection on synthetic time series under the random slide window (RSW) and fixed slide window (FSW) frameworks. In the proposed WEDM method, a concept of normalized error distance was introduced that allows comparisons of the distance between the estimated change-point (eCP) position and the target change point (tCP) in the synthetic time series. In the successive MCPs detection, the proposed WEDM method first divides the original time-series sample into a series of data segments in terms of the assigned tCPs set and then calculates a normalized error distance (NED) value for each segment. Next, our WEDM presents the frequency and WED distribution of the resultant eCPs from all data segments in the normalized positive-error distance (NPED) and the normalized negative-error distance (NNED) intervals in the same coordinates. Last, the mean WED (MWED) and MWTD (1-MWED) were obtained and then dealt with as important performance evaluation indexes. Based on the synthetic datasets in the Matlab platform, repetitive tests on single CP detection were executed by using different CPD models, including ternary search tree (TST), binary search tree (BST), Kolmogorov–Smirnov (KS) tests, t-tests (T), and singular spectrum analysis (SSA) algorithms. Meanwhile, successive tests on MCPs detection were implemented under the fixed slide window (FSW) and random slide window (RSW) frameworks. These CPD models mentioned above were evaluated in terms of our WED metrics, together with supplementary indexes for evaluating the convergence of different CPD models, including rates of hit, miss, error, and computing time, respectively. The experimental results showed the value of this WEDM method.

Spatio-Temporal Dynamics of Noon-Time Temperature in Selected Cities in Sudan Savanna and Tropical Rainforest Zones of Nigeria

Urban centres in Sub-Saharan Africa have been undergoing unprecedented urbanization in the past decades at annual rates of almost 4%; with attendant impacts on the cities’ thermal conditions. This study aimed at characterizing the noon-time maximum temperature of two selected cities each in the Sudan and Tropical Rainforest zones of Nigeria. The study utilized daily ERA Interim (European Reanalysis) grid-based 2 meter above ground daily noontime maximum temperature (°C) data of the European Centre for Medium-range Weather Forecasts (ECMWF) from 1990 to 2019. R Statistical package version 3.6.1 was employed to detect the trend and seasonality in the maximum noon-time temperature of the four cities using non-parametric Mann-Kendall trend and seasonal trend tests. The statistical properties of the data were first analyzed by graphical examination of the data, using time plots, and boxplots. Also, the normality test of Shapiro-Wilk (S-W test) was applied. Pettitt test was then employed to test for single change-point detection in the temperature series. The study revealed higher mean temperature values of 27.49°C and 25.56°C respectively for Birnin Kebbi and Kano both in the Sudan, and lower temperature values of 24.08°C and 23.17°C respectively for Ibadan and Owerri located in the Tropical rainforest. The Tau statistics for Kano, Ibadan and Owerri are 0.07084, 0.09848 and 0.09113 and the corresponding p-values are 0.0447, 0.0053 and 0.0098 which are less than 0.05 alpha value; indicating significant trends for the three cities. The results also show significant seasonal increase at 0.05 significant levels in the maximum noon-time temperature series for all the locations. The study recommends urban landscape planning and design for optimization of outdoor thermal comfort and creation of heathier urban environments for the city dwellers.

Segmentation Method for Ship-Radiated Noise Using the Generalized Likelihood Ratio Test on an Ordinal Pattern Distribution.

Due to the diversity of ship-radiated noise (SRN), audio segmentation is an essential procedure in the ship statuses/categories identification. However, the existing segmentation methods are not suitable for the SRN because of the lack of prior knowledge. In this paper, by a generalized likelihood ratio (GLR) test on the ordinal pattern distribution (OPD), we proposed a segmentation criterion and introduce it into single change-point detection (SCPD) and multiple change-points detection (MCPD) for SRN. The proposed method is free from the acoustic feature extraction and the corresponding probability distribution estimation. In addition, according to the sequential structure of ordinal patterns, the OPD is efficiently estimated on a series of analysis windows. By comparison with the Bayesian Information Criterion (BIC) based segmentation method, we evaluate the performance of the proposed method on both synthetic signals and real-world SRN. The segmentation results on synthetic signals show that the proposed method estimates the number and location of the change-points more accurately. The classification results on real-world SRN show that our method obtains more distinguishable segments, which verifies its effectiveness in SRN segmentation.

Single change-point detection methods for small lifetime samples

In this paper, we address the problem of deciding if either n consecutive independent failure times have the same failure rate or if there exists some \(k\in \{1,\ldots ,n\}\) such that the common failure rate of the first k failure times is different from the common failure rate of the last \(n-k\) failure times, based on an exponential lifetime distribution. The statistical test we propose is based on the empirical average ratio under the assumption of exponentiality. The proposed test is compared to the one based on the Mann–Whitney statistic for which no parametric assumption on the underlying distribution is necessary. The proposed statistics are free of the unknown underlying distribution under the null hypothesis of homogeneity of the n failure times which enables the determination of critical values of the proposed tests by Monte Carlo methods for small sample sizes.

Bayesian single change point detection in a sequence of multivariate normal observations

A Bayesian method is used to see whether there are changes of mean, covariance, or both at an unknown time point in a sequence of independent multivariate normal observations. Noninformative priors are used for all competing models: no-change model, mean change model, covariance change model, and mean and covariance change model. We use several versions of the intrinsic Bayes factor of Berger and Pericchi (Berger, J.O. and Pericchi, L.R., 1996, The intrinsic Bayes factor for model selection and prediction. Journal of the American Statistical Association,\\/ 91, 109–122; Berger, J.O. and Pericchi, L.R., 1998, Accurate and stable Bayesian model selection: the median intrinsic Bayes factor. Sankhya Series B, 60, 1–18.) to detect a change point. We demonstrate our results with some simulated datasets and a real dataset.

Trend test and change-point detection for the annual discharge series of the Yangtze River at the Yichang hydrological station / Test de tendance et détection de rupture appliqués aux séries de débit annuel du fleuve Yangtze à la station hydrologique de Yichang

The trend test and change-point analysis have been carried out on several annual discharge series of the Yangtze River at the Yichang hydrological station, including the discharge series of the annual maximum, annual minimum and annual mean during the period 1882–2001. The results of both the Mann-Kendall and Spearman’s rho trend tests show that, at the 5% significance level, the annual maximum flood series did not have any statistically significant trend, but the annual minimum flow series and the annual mean discharge series exhibited a sign of decreasing trend. For single change-point detection, a Bayesian model was established to study the abrupt change in the mean levels of the time series. Given the observed hydrological data, the Bayesian model can estimate the posterior probability distribution of each change-point location by using the Monte Carlo Markov Chain (MCMC) sampling method. The results of the Bayesian model show that, during the past 120 years, the mean levels of both the annual minimum discharge series and the annual mean discharge series have decreased by 8% and 6% respectively. Further analysis suggested that, for the annual minimum discharge series and the annual mean discharge series, both the trend term and the abrupt change term are very closely related and very hard to distinguish from each other.