Potential Change Points Research Articles

Analysis of spatiotemporal variation in land surface temperature on the Tibetan Plateau from 2001 to 2020

ABSTRACT With global climate warming intensifying, the Land Surface Temperature (LST) variation on the Tibetan Plateau (TP) has become a hot topic in environmental studies. This letter employs spatial analysis to identify LST distribution characteristics, the Pettitt test to detect abrupt changes, and Fast Fourier Transform (FFT) to analyse periodic variations. Analysing mean annual and seasonal LST from 2001 to 2020, the results indicate the following: (1) Over the past 20 years, the TP’s LST increased slowly at 0.08°C per decade, with significant seasonal variations. Warming trends dominate in spring, summer, and autumn, shifting from the northern to the southwestern plateau. Autumn shows the most significant warming at 0.31°C per decade, while winter shows a cooling trend at −0.46°C per decade. (2) The Pettitt test reveals no statistically significant abrupt changes in mean annual and seasonal LST, though potential change points were detected in 2013 for mean annual LST, and in 2005, 2006, 2014, and 2017 for summer, spring, autumn, and winter, respectively. This indicates relative stability in interannual temperature changes, with some asynchronous seasonal variations. FFT analysis indicates dominant short-term variability with a period of 3.33 years and secondary cycles of 10 and 5 years.

A two-stage monitoring scheme for multiple high-dimensional data streams

With the rapid development of data acquisition and analysis technology, the online monitoring of data streams is particularly important in modern industries. This study proposes an efficient online monitoring scheme for multiple high-dimensional data streams. We first construct a point-wise process monitoring control chart based on statistical extreme value theory. Then we use the clustering method to roughly obtain reliable data streams and suspected abnormal data streams, within the sliding window range, further identify abnormal data streams one by one over time points, and estimate the potential change points of these abnormal streams. Finally, we conduct simulations and case studies on this method, and compare it with existing competitive methods to demonstrate its effectiveness.

What makes a real change in software performance? An empirical study on analyzing the factors that affect the triagement of performance change points

Performance tests can be automatically done on each commit version with a continuous integration system. After code changes are pushed to the repository, multiple benchmark tests are run to measure system's performance. Change point detection technology analyzes all these outcomes to identify commits that significantly change performance automatically. However, a considerable number of automatically detected change points are tagged as not being actionable (false positive). Typically, validating potential change points by hand is difficult, time-consuming, and thus creates a bottleneck in the testing process.Our work focuses on identifying what factors affect performance change point triagement and triaging whether a newly detected change point is true positive or not automatically. We start by extracting 34 features from four dimensions i.e., Configuration, Time Series, Version, and Context. We utilize a random forest classifier to triage the change points based on the proposed features. The results indicate that most of the proposed features differ significantly between true positive and false positive change points. On average, our model obtains an AUC of 0.881, which is statistically considerably better than two state-of-the-art approaches. We also look into the most important features for triagement and discover that version related features are the most essential factors.

Time series based road traffic accidents forecasting via SARIMA and Facebook Prophet model with potential changepoints

Road traffic accident (RTA) is a critical global public health concern, particularly in developing countries. Analyzing past fatalities and predicting future trends is vital for the development of road safety policies and regulations. The main objective of this study is to assess the effectiveness of univariate Seasonal Autoregressive Integrated Moving Average (SARIMA) and Facebook (FB) Prophet models, with potential change points, in handling time-series road accident data involving seasonal patterns in contrast to other statistical methods employed by key governmental agencies such as Ghana's Motor Transport and Traffic Unit (MTTU). The aforementioned models underwent training with monthly RTA data spanning from 2013 to 2018. Their predictive accuracies were then evaluated using the test set, comprising monthly RTA data from 2019. The study employed the Box-Jenkins method on the training set, yielding the development of various tentative time series models to effectively capture the patterns in the monthly RTA data. SARIMA(0,1,1)×(1,0,0)12 was found to be the suitable model for forecasting RTAs with a log-likelihood value of −266.28, AIC value of 538.56, AICc value of 538.92, BIC value of 545.35. The findings disclosed that the SARIMA(0,1,1)×(1,0,0)12 model developed outperforms FB-Prophet with a forecast accuracy of 93.1025% as clearly depicted by the model's MAPE of 6.8975% and a Theil U1 statistic of 0.0376 compared to the FB-Prophet model's respective forecasted accuracy and Theil U1 statistic of 84.3569% and 0.1071. A Ljung-Box test on the residuals of the estimated SARIMA(0,1,1)×(1,0,0)12 model revealed that they are independent and free from auto/serial correlation. A Box-Pierce test for larger lags also revealed that the proposed model is adequate for forecasting. Due to the high forecast accuracy of the proposed SARIMA model, the study recommends the use of the proposed SARIMA model in the analysis of road traffic accidents in Ghana.

Study on a mother wavelet optimization framework based on change-point detection of hydrological time series

Abstract. Hydrological time series (HTS) are the key basis of water conservancy project planning and construction. However, under the influence of climate change, human activities and other factors, the consistency of HTS has been destroyed and cannot meet the requirements of mathematical statistics. Series division and wavelet transform are effective methods to reuse and analyse HTS. However, they are limited by the change-point detection and mother wavelet (MWT) selection and are difficult to apply and promote in practice. To address these issues, we constructed a potential change-point set based on a cumulative anomaly method, the Mann–Kendall test and wavelet change-point detection. Then, the degree of change before and after the potential change point was calculated with the Kolmogorov–Smirnov test, and the change-point detection criteria were proposed. Finally, the optimization framework was proposed according to the detection accuracy of MWT, and continuous wavelet transform was used to analyse HTS evolution. We used Pingshan station and Yichang station on the Yangtze River as study cases. The results show that (1) change-point detection criteria can quickly locate potential change points, determine the change trajectory and complete the division of HTS and that (2) MWT optimal framework can select the MWT that conforms to HTS characteristics and ensure the accuracy and uniqueness of the transformation. This study analyses the HTS evolution and provides a better basis for hydrological and hydraulic calculation, which will improve design flood estimation and operation scheme preparation.

A Novel Method for Automatic Detection and Elimination of the Jumps Caused by the Instantaneous Disturbance Torque in the Maglev Gyro Signal

The signal measured by the maglev gyro sensor is sensitive to the influence of the instantaneous disturbance torque caused by the instantaneous strong wind or the ground vibration, which reduced the north-seeking accuracy of the instrument. To address this issue, we proposed a novel method combining the heuristic segmentation algorithm (HSA) and the two-sample Kolmogorov-Smirnov (KS) test (named HSA-KS method) to process the gyro signals and improve the north-seeking accuracy of the gyro. There were two key steps in the HSA-KS method: (i) all the potential change points were automatically and accurately detected by HSA, and (ii) the jumps in the signal caused by the instantaneous disturbance torque were quickly located and eliminated by the two-sample KS test. The effectiveness of our method was verified through a field experiment on a high-precision global positioning system (GPS) baseline at the 5th sub-tunnel of the Qinling water conveyance tunnel of the Hanjiang-to-Weihe River Diversion Project in Shaanxi Province, China. Our results from the autocorrelograms indicated that the jumps in the gyro signals can be automatically and accurately eliminated by the HSA-KS method. After processing, the absolute difference between the gyro and high-precision GPS north azimuths was enhanced by 53.5%, which was superior to the optimized wavelet transform and the optimized Hilbert-Huang transform.

A Non-Parametric Approach for Change-Point Detection of Multi-Parameters in Time-Series Data

Change-point analysis of time-series data plays a vital role in various fields of earth sciences under changing environments. Most of the analysis approaches were usually designed to detect the change-point in the level of time-series mean. In this study, we aimed to propose a non-parametric approach to detect the change-point of different parameters of time-series data. In this approach, the Boot- strap method, coupling with Kernel density estimation, was first used to estimate the probability distribution function (pdf) of a parameter before and after any potential change-points. Second, the Ar-index based on the uncross area of the two pdfs was designed to quantify the difference of the parameter before and after each potential change-point. Finally, the potential change-point owning the largest Ar-index value was determined as the locations of the change-point of the parameter. The hydrological extreme series from four stations in the Hanjiang basin were used to demonstrate this approach. The Pettitt test method commonly used in hydrology was employed as a comparison to indirectly analyze the reliability of the proposed approach. The results show that change-point detected by the proposed approach in the four stations are identified with those detected by the Pettitt approach in the level of time-series mean. But in comparison with the Pettitt test, the proposed approach can provide more detection information for other parameters, such as coefficient of variation (Cv) and coefficient of skewness (Cs) of the series. The results also show that the degree of change in the series mean is greater than its Cv and Cs, while the degree of change in series Cv is greater than its Cs.

State-domain change point detection for nonlinear time series regression

Change point detection in time series has attracted substantial interest, but most of the existing results have been focused on detecting change points in the time domain. This paper considers the situation where nonlinear time series have potential change points in the state domain. We apply a density-weighted anti-symmetric kernel function to the state domain and therefore propose a nonparametric procedure to test the existence of change points. When the existence of change points is affirmative, we further introduce an algorithm to estimate the number of change points together with their locations. Theoretical results of the proposed detection and estimation procedures are given and a real dataset is used to illustrate our methods.

Climate teleconnections, interannual variability, and evolution of the rainfall regime in a tropical Caribbean island: case study of Barbados

A limited number of studies have focused on the hydroclimate dynamics of tropical Caribbean islands. The present study aims to analyze the rainfall regime in Barbados. CHIRPS gridded dataset, at a resolution of 0.05°×0.05°, providing daily rainfall data from January 1981 until 2018 was used. The variables analyzed were the annual and seasonal maximum rainfall, the total annual and seasonal rainfall, and the number of rainy days per year and per season. Potential change points in rainfall time-series were detected with a Bayesian multiple change point detection procedure. Time series were then analyzed for detection of trends using the modified Mann-Kendall test. The true temporal slopes of the rainfall time series were obtained with the Theil-Sen’s statistic. The links between rainfall and various global climate oscillation indices were also investigated. Results indicate that no change points or significant trends were observed in the annual rainfall time series. However, it was found that some climate indices have a strong correlation with precipitation on the island, especially for the total rainfall and the number of rainy days. A stationary and non-stationary frequency analysis is carried out on the rainfall annual variables using climate oscillation indices as covariates, and uncertainties on quantile estimates are identified. It is shown that non-stationary models lead to a better fit to rainfall data. Empirical mode decomposition (EMD) is used for the long-term prediction of hydro-climatic time series. Rainfall annual time series were extended with this method for a period of 20 years. Results indicate that, within that period, annual maximum rainfall will increase by about 12 mm (or 0.6 mm/year), total annual rainfall will increase by about 200 mm (or 10 mm/year) and the number of rainy days per year will see a slight decrease by about 3 days (or 0.15 day/year).

Multiple change point detection and validation in autoregressive time series data

It is quite common that the structure of a time series changes abruptly. Identifying these change points and describing the model structure in the segments between these change points is of interest. In this paper, time series data is modelled assuming each segment is an autoregressive time series with possibly different autoregressive parameters. This is achieved using two main steps. The first step is to use a likelihood ratio scan based estimation technique to identify these potential change points to segment the time series. Once these potential change points are identified, modified parametric spectral discrimination tests are used to validate the proposed segments. A numerical study is conducted to demonstrate the performance of the proposed method across various scenarios and compared against other contemporary techniques.

Change Point Detection with Mean Shift Based on AUC from Symmetric Sliding Windows

Change point detection is widely used in signal detection, industrial engineering, economy, finance, biomedicine and many other fields. The widely used parametric methods require prior knowledge of the noise signal distribution, which are seldom realistic. In practice, when the distribution of noise is not known, it is desirable to design algorithms based on non-parametric statistics, which, in the null case (no change point), are completely distribution free. To this end, we propose to use two symmetric sliding windows to compute the Area Under the receiver operating characteristic Curve (AUC) as a test statistic to measure the difference between the distribution of two samples. In the stage of change point detection, a threshold is designed according to hypothesis test which is based on the null distribution of the test statistics. This threshold is used to detect the potential change points in the signal. To reduce the probability of false alarm detection, a key parameter K is set to distinguish and delete the false alarms in potential change points. Comparative studies showed that our proposed method outperforms the classical Relative unconstrained Least-Squares Importance Fitting (RuLSIF) algorithm and is also better than the Hawkins, Qiu, and Kang (HQK) algorithm when the noise follows non-normal distributions.

Responses of Baseflow to Ecological Construction and Climate Change in Different Geomorphological Types in The Middle Yellow River, China

Baseflow is a critical component of streamflow in arid areas. Determining variations in baseflow and the factors affecting it have positive roles for water resource utilization in arid watersheds. Two watersheds, the Hailiutu River watershed (HLTR) and the Dali River watershed (DLR), located in two different geomorphological regions of the middle Yellow River, were selected for this study. By using the Eckhardt segment method (fourth digital filtering method, DF4), baseflow was separated from streamflow based on its daily data. Mann-Kendall trend test analysis (M-K trend test) was used to test the trends in baseflow change at different times. Complex Morlet wavelet analysis was used to judge baseflow periodicity. Heuristic segmentation and sequential cluster analysis were used to identify the potential change points in the baseflow series for the two regions together with Pearson correlation coefficient. The results showed: (1) the annual baseflow of the HLTR and the DLR showed significantly decreasing trends (P < 0.01), more significantly for the HLTR (0.33 × 108 m3) than the DLR (0.20 × 108 m3). The annual base flow index (BFI, baseflow/total streamflow) in the wind-sand region (0.75) was larger than for the loess region (0.55), and the BFI in the wind-sand region was more stable in different periods. (2) The annual baseflow of the HLTR and the DLR both exhibited a complete main cycle of 42 years and 38 years, respectively. The change points of the annual baseflow in the HLTR were 1967 and 1986, and 1971 and 1996 in the DLR. (3) There was no significant change in annual precipitation in the two watersheds, while annual reference evapotranspiration (ET0) in the DLR showed a significant increasing trend (P < 0.01). The normalized difference vegetation index (NDVI) on the DLR (0.40) was higher than on the HLTR (0.26). (4) Baseflow in the wind-sand region, where vegetation improvement was the only ecological activity, decreased faster than in the loess region where there had been numerous ecological measures such as vegetation improvement, check dams and terraces. This implied that comprehensive measures such as these were helpful in slowing the rate at which the baseflow decreases. Therefore, the effect of ecological construction should be considered in future baseflow studies in other geomorphological types within the Middle Yellow River Basin.

No Sign of G2's Encounter Affecting Sgr A*'s X-Ray Flaring Rate from Chandra Observations

Abstract An unusual object, G2, had its pericenter passage around Sgr A*, the 4 × 106 M ⊙ supermassive black hole in the Galactic Center, in Summer 2014. Several research teams have reported evidence that, following G2's pericenter encounter, the rate of Sgr A*'s bright X-ray flares increased significantly. Our analysis carefully treats varying flux contamination from a nearby magnetic neutron star and is free from complications induced by using data from multiple X-ray observatories with different spatial resolutions. We test the scenario of an increased bright X-ray flaring rate using a massive data set from the Chandra X-ray Observatory, the only X-ray instrument that can spatially distinguish between Sgr A* and the nearby Galactic Center magnetar throughout the full extended period encompassing G2's encounter with Sgr A*. We use X-ray data from the 3 Ms observations of the Chandra X-ray Visionary Program (XVP) in 2012, as well as an additional 1.5 Ms of observations up to 2018. We use detected flares to make distributions of flare properties. Using simulations of X-ray flares accounting for important factors such as the different Chandra instrument modes, we test the null hypothesis on Sgr A*'s bright (or any flare category) X-ray flaring rate around different potential change points. In contrast to previous studies, our results are consistent with the null hypothesis; the same model parameters produce distributions consistent with the observed ones around any plausible change point.

A quantitative assessment of hydrological responses to climate change and human activities at spatiotemporal within a typical catchment on the Loess Plateau, China

It is important to understand the relative contributions of climate change and human activities to changes in runoff to sustainably manage water resources in the arid Loess Plateau, China. In this study, Chabagou River Basin in the central arid region of the Loess Plateau was selected to investigate changes in runoff, within which a series of soil conservation measures have been implemented since the late 1950s. We applied the non-parametric Kendall test (MK) and the Bayesian change point (BCP) method to identify trends and potential change points in hydro-meteorological data sequences. The results of the MK test revealed no significantly abrupt variation has been detected in annual hydro-meteorological data sequences, while a number of potential change points were identified using the BCP method applying different posterior probabilities. We also systematically review two commonly applied quantitative methods that draw on both empirical statistics and hydrological modeling to quantify the impact of climate change, human activities and meteorological variation on mean annual runoff at spatiotemporal scales based on precipitation, evapotranspiration, runoff-precipitation coefficients, and soil water throughout the river basin. The results of this study show that climate change and normal climate variability are responsible for about 80% of the decrease in runoff, mainly due to reduced precipitation, while human activities was responsible for <20% of reductions in runoff. The results also show that soil conservation measures have influenced hydrological processes at spatiotemporal and that runoff within the Chabagou River Basin (CRB) is more sensitive to spatial distribution of soil conservation measures than meteorological factors. The relative contributions to runoff variations that derive from climate change, human activities and meteorological variation were calculated in this study, but interactions between climate change and human activities is complex, and not easy to be separated.

Identification of the Non-stationarity of Floods: Changing Patterns, Causes, and Implications

The assumption of stationarity in the flood time series is the basis for flood design and forecasting. Therefore, identification of the non-stationarity of flood series and the underlying causes is necessary for flood risk and water resources management. The Wei River Basin (WRB) of China was selected as the case study. Nonstationary flood behavior was examined comprehensively in terms of trends and the mean and variance change point. Then, the implications of the nonstationary flood series were explored. Furthermore, the impacts of antecedent precipitation, El Nino Southern Oscillation/Pacific Decadal Oscillation and vegetation coverage on floods were investigated. The results indicated following: (1) There is a non-significant delay in the timing of the annual maximum flood peak and seasonal floods across the basin; (2) the assumption of stationarity in the flood series is invalid, with significant downward trends and change points identified; (3) bias arising from the variance change point is much more significant than that of the mean change point in estimating floods; and (4) changing climate and human activities are jointly responsible for nonstationary floods in the WRB. These findings provide new insights into nonstationary flood behavior by emphasizing the importance of identifying the potential variance change points in the flood series, which is important for flood mitigation and water resources management.

Identifying critical limits in oil palm cover for the conservation of terrestrial mammals in Colombia

As oil palm plantations continue to expand in Neotropical regions, identifying critical transitions in land use, at which animal communities can be drastically altered, is crucial for conservation planning. Here, we investigated potential unexpected change points (thresholds) in the response of terrestrial mammal's richness and community composition to increasing oil palm cover in the Llanos region of Colombia. We deployed camera traps to detect species across 56 sites (landscapes of ~220 ha each) and used segmented regression and Threshold Indicator Taxa Analysis (TITAN) for the identification of these thresholds. We found a negative linear relationship between the proportion of oil palm and species richness, but no evidence of a threshold. In contrast, we found strong signs of a community threshold when oil palm cover in the study area reached 45–75%, at which mammalian species composition (taxon-specific changes of abundance and occurrence frequency) drastically changed. When species were assessed individually, a significant threshold relationship to oil palm cover was found to occur in 10 of the 15 examined species, with four (squirrel, agouti, spiny rat, common opossum) having a negative drastic change at approximately 45% oil palm cover. Five species showed no evidence for any critical threshold (giant and lesser anteater, jaguarondi, white-tailed deer and raccoon). We used the community threshold identified above as a baseline to evaluate the conservation status of the four oil palm production zones in Colombia. We found that approximately 41% of the total area covered by oil palm in Colombia has crossed the identified threshold of 45–75%, suggesting urgent need for forest restoration to increase its extent if a collapse of their resident mammal communities is to be avoided. These findings provide guidance for the design of sustainable landscapes within production areas in Colombia to promote the conservation of terrestrial mammals.

Retrospective analysis for phase I statistical process control and process capability study using revised sample entropy

This study explored a new nonparametric analytical method for identifying heterogeneous segments in time-series data for data-abundant processes. A sample entropy (SampEn) algorithm often used in signal processing and information theory can also be used in a time series or a signal stream, but the original SampEn is only capable of quantifying process variation changes. The proposed algorithm, the adjusted sample entropy (AdSEn), is capable of identifying process mean shifts, variance changes, or mixture of both. A simulation study showed that the proposed method is capable of identifying heterogeneous segments in a time series. Once segments of change points are identified, any existing change-point algorithms can be used to precisely identify exact locations of potential change points. The proposed method is especially applicable for long time series with many change points. Properties of the proposed AdSEn are provided to demonstrate the algorithm’s multi-scale capability. A table of critical values is also provided to help users accurately interpret entropy results.

Bayesian Inventory Management with Potential Change‐Points in Demand

We consider the inventory management problem of a firm reacting to potential change points in demand, which we define as known epochs at which the demand distribution may (or may not) abruptly change. Motivating examples include global news events (e.g., the 9/11 terrorist attacks), local events (e.g., the opening of a nearby attraction), or internal events (e.g., a product redesign). In the periods following such a potential change point in demand, a manager is torn between using a possibly obsolete demand model estimated from a long data history and using a model estimated from a short, recent history. We formulate a Bayesian inventory problem just after a potential change point. We pursue heuristic policies coupled with cost lower bounds, including a new lower bounding approach to non‐perishable Bayesian inventory problems that relaxes the dependence between physical demand and demand signals and that can be applied for a broad set of belief and demand distributions. Our numerical studies reveal small gaps between the costs implied by our heuristic solutions and our lower bounds. We also provide analytical and numerical sensitivity results suggesting that a manager worried about downside profit risk should err on the side of underestimating demand at a potential change point.

Bayesian P-splines and advanced computing in R for a changepoint analysis on spatio-temporal point processes

ABSTRACTThis work presents advanced computational aspects of a new method for changepoint detection on spatio-temporal point process data. We summarize the methodology, based on building a Bayesian hierarchical model for the data and declaring prior conjectures on the number and positions of the changepoints, and show how to take decisions regarding the acceptance of potential changepoints. The focus of this work is about choosing an approach that detects the correct changepoint and delivers smooth reliable estimates in a feasible computational time; we propose Bayesian P-splines as a suitable tool for managing spatial variation, both under a computational and a model fitting performance perspective. The main computational challenges are outlined and a solution involving parallel computing in R is proposed and tested on a simulation study. An application is also presented on a data set of seismic events in Italy over the last 20 years.

A changepoint statistic with uniform type I error probabilities

ABSTRACTLikelihood ratio tests for a change in mean in a sequence of independent, normal random variables are based on the maximum two-sample t-statistic, where the maximum is taken over all possible changepoints. The maximum t-statistic has the undesirable characteristic that Type I errors are not uniformly distributed across possible changepoints. False positives occur more frequently near the ends of the sequence and occur less frequently near the middle of the sequence. In this paper we describe an alternative statistic that is based upon a minimum p-value, where the minimum is taken over all possible changepoints. The p-value at any particular changepoint is based upon both the two-sample t-statistic at that changepoint and the probability that the maximum two-sample t-statistic is achieved at that changepoint. The new statistic has a more uniform distribution of Type I errors across potential changepoints and it compares favorably with respect to statistical power, false discovery rates, and the mean square error of changepoint estimates.