Change Point Test Research Articles

Single Change-point Tests for P-order Autoregressive Models

Single Change-point Tests for P-order Autoregressive Models

Approximate filtering of conditional intensity process for Poisson count data: Application to urban crime

The primary focus is a sequential data assimilation method for count data modelled by an inhomogeneous Poisson process. In particular, a quadratic approximation technique similar to the extended Kalman filter is applied to develop a sub-optimal, discrete-time, filtering algorithm, called the extended Poisson–Kalman filter (ExPKF), where only the mean and covariance are sequentially updated using count data via the Poisson likelihood function. The performance of ExPKF is investigated in several synthetic experiments where the true solution is known. In numerical examples, ExPKF provides a good estimate of the “true” posterior mean, which can be well-approximated by the particle filter (PF) algorithm in the very large sample size limit. In addition, the experiments demonstrate that the ExPKF algorithm can be conveniently used to track parameter changes; on the other hand, a non-filtering framework such as a maximum likelihood estimation (MLE) would require a statistical test for change points or implement time-varying parameters. Finally, to demonstrate the model on real-world data, the ExPKF is used to approximate the uncertainty of urban crime intensity and parameters for self-exciting crime models. The Chicago Police Department’s CLEAR (Citizen Law Enforcement Analysis and Reporting) system data is used as a case study for both univariate and multivariate Hawkes models. An improved goodness of fit measured by the Kolmogorov–Smirnov (KS) statistics is achieved by the filtered intensity. The potential of using filtered intensity to improve police patrolling prioritisation is also tested. By comparing with the prioritisation based on MLE-derived intensity and historical frequency, the result suggests an insignificant difference between them. While the filter is developed and tested in the context of urban crime, it has the potential to make a contribution to data assimilation in other application areas.

A fully flexible changepoint test for regression models with stationary errors

A fully flexible changepoint test for regression models with stationary errors

Nuisance-parameter-free changepoint detection in non-stationary series

Many changepoint detection procedures rely on the estimation of nuisance parameters (like long-run variance). If a change has occurred, estimators might be biased and data adaptive rules for the choice of tuning parameters might not work as expected. If the data are not stationary, this becomes more challenging. The aim of this paper is to present two changepoint tests, which involve neither nuisance nor tuning parameters. This is achieved by combing self-normalization and wild bootstrap. We investigate the asymptotic behavior and show the consistency of the bootstrap under the hypothesis as well as under the alternative, assuming mild conditions on the weak dependence of the time series. As a by-product, a changepoint estimator is introduced and its consistency is proved. The results are illustrated through a simulation study. The new completely data-driven tests are applied to real data examples from finance and hydrology.

A New Class of Change Point Test Statistics of Rényi Type

A new class of change point test statistics is proposed that utilizes a weighting and trimming scheme for the cumulative sum (CUSUM) process inspired by Rényi. A thorough asymptotic analysis and simulations both demonstrate that this new class of statistics possess superior power compared to traditional change point statistics based on the CUSUM process when the change point is near the beginning or end of the sample. Generalizations of these “Rényi” statistics are also developed to test for changes in the parameters in linear and nonlinear regression models, and in generalized method of moments estimation. In these contexts, we applied the proposed statistics, as well as several others, to test for changes in the coefficients of Fama–French factor models. We observed that the Rényi statistic was the most effective in terms of retrospectively detecting change points that occur near the endpoints of the sample.

Considering long‐memory when testing for changepoints in surface temperature: A classification approach based on the time‐varying spectrum

AbstractChangepoint models are increasingly used to represent changes in the rate of warming in surface temperature records. On the opposite hand, a large body of literature has suggested long‐memory processes to characterize long‐term behavior in surface temperatures. While these two model representations provide different insights into the underlying mechanisms, they share similar spectrum properties that create “ambiguity” and challenge distinguishing between the two classes of models. This study aims to compare the two representations to explain temporal changes and variability in surface temperatures. To address this question, we extend a recently developed time‐varying spectral procedure and assess its accuracy through a synthetic series mimicking observed global monthly surface temperatures. We vary the length of the synthetic series to determine the number of observations needed to be able to accurately distinguish between changepoints and long‐memory models. We apply the approach to two gridded surface temperature data sets. Our findings unveil regions in the oceans where long‐memory is prevalent. These results imply that the presence of long‐memory in monthly sea surface temperatures may impact the significance of trends, and special attention should be given to the choice of model representing memory (short versus long) when assessing long‐term changes.

Change-point analysis of the failure mechanisms based on accelerated life tests

In the accelerated life tests, the common failure mechanism is considered as a necessary condition for the extrapolated procedure. The traditional extrapolation model may become unreliable if the failure mechanisms under the accelerated stress levels are different from that under the normal operating condition. In this paper, we propose a change-point model for the coefficients of variation to fit the abrupt change behavior of the failure mechanisms with a nonparametric empirical likelihood approach. The related statistical inferences of the proposed model are studied to test whether there exists a change and estimate the corresponding location of the change. Monte Carlo simulations are conducted to investigate the performance of the proposed change-point test model. For the small sample data, a bootstrapping method is presented as an alternative detecting procedure. The detailed calculation process is illustrated by the lifetime data of the metal oxide semiconductor transistors in the power distribution system of Chinese Tiangong aircrafts.

Responses of streamflow to vegetation and climate change in southwestern Australia

Southwestern Australia has experienced recent climate change, with an increase in air temperature of 0.6 °C and a reduction in mean annual precipitation of −15% since 1970. Along with the warming and drying trends, dramatic declines of streamflow have occurred across the region. However, both forest mortality and an increase in leaf area index have been observed in the southwestern forest, suggesting varied responses of vegetation to climate change. In this study, 30 catchments were analyzed using the Mann-Kendall trend test, Pettitt’s change point test and the theoretical framework of the Budyko curve to study the rainfall-runoff relationship change, and effects of climate and land cover change on streamflow. A declining trend and relatively consistent change point (2000) of streamflow were found in most catchments, with 14 catchments showing significant declines (p < 0.05, −68.1% to −35.6%) over 1970–2000 and 2001–2015. Most of the catchments have been shifting towards a more water-limited climate condition since 2000. For the period 1970 to 2015, the dynamic of vegetation attributes (land cover/use change and growth of vegetation) dominated the decrease of streamflow in about half the study catchments. In general, a coequal role of climate and vegetation on the decline in streamflow was found in the study, suggesting the importance of vegetation management on future water management and production. Precipitation is predicted to decline in the future; therefore, some forest management intervention is required to maintain forest growth and water supply in the southwest of Australia.

Copula-based dynamic models for multivariate time series

In this paper, we propose an intuitive way to couple several dynamic time series models even when there are no innovations. This extends previous work for modeling dependence between innovations of stochastic volatility models. We consider time-dependent and time-independent copula models and we study the asymptotic behavior of some empirical processes constructed from pseudo-observations, as well as the behavior of maximum pseudo-likelihood estimators of the associated copula parameters. The results show that even if the univariate dynamic models depend on unknown parameters, the limiting behavior of many processes of interest does not depend on the estimation errors. One can perform tests for change points on the full distribution, the margins or the copula, as if the parameters of the dynamic models were known. This is also true for some parametric models of time-dependent copulas. This interesting property makes it possible to construct consistent tests of specification for the dependence models, without having to consider the dynamic time series models. Monte Carlo simulations are used to demonstrate the power of the proposed goodness-of-fit test in finite samples. An application to financial data is given.

Impact of Climate Variabilities and Human Activities on Surface Water Extents in Reservoirs of Yongding River Basin, China, from 1985 to 2016 Based on Landsat Observations and Time Series Analysis

Yongding River is the largest river flowing through Beijing, the capital city of China. In recent years, Yongding River Basin (YDRB) has witnessed increasing human impacts on water resources, posing serious challenges in hydrological and ecological health. In this study, remote sensing techniques and statistical time series approaches for hydrological studies were combined to characterize the dynamics and driving factors of reservoir water extents in YDRB during 1985–2016. First, 107 Landsat 4, 5, 7 and 8 images were used to extract surface water extents in YDRB during 1985–2016 using a combination of water indices and Otsu threshold algorithm. Significant positive correlation was found between water extents and the annual inflow for the two biggest reservoirs, the downstream Guanting and upstream Cetian reservoirs, proving their representativeness of surface water availability in this basin. Then, statistical time series approaches including trend-free pre-whitening Mann-Kendall trend test, Pettit change-point test and double mass curve method, which are frequently used in hydrological studies, were adopted to quantify the trend of reservoir water extents dynamics and the relative contributions of climate variability and human activities. Results showed that the water extents in both reservoirs exhibited significant downward trend with change point occurring in 2001 and 2005 for Guanting and Cetian, respectively. About 74%~75% of the shrinkage during the post-change period can be attributed to human activities, among which GDP, population, electricity power production, raw coal production, steel and crude iron production, value of agriculture output, and urban area were the major human drivers. Hydrological connectivity between the upstream Cetian and downstream Guanting reservoirs declined during the post-change period. Since 2012, water extents in both reservoirs recovered as a result of various governmental water management policies including the South-to-North Water Diversion Project. The methodology presented in this study can be used for analyzing the dynamics and driving mechanism of surface water resources, especially for un-gauged or poorly-gauged watersheds.

A Self‐Normalized Semi‐Parametric Test to Detect Changes in the Long Memory Parameter

We consider the problem of testing for change points in the long memory parameter. The test relies on semi‐parametric estimation of the long memory parameter, which does not require the complete parametric specification of the whole spectrum. A self‐normalizer utilizing a sequence of recursive semi‐parametric estimators is used to make the asymptotic distribution of the test statistic free of the nuisance scale parameter. We study the asymptotic behavior of the proposed test for situations when there is at most one change point and also when there are an unknown number of change points. Monte Carlo simulations are carried out to examine the finite‐sample performance of the proposed test.

Poisson Quasi-Maximum Likelihood Estimator-based CUSUM Test for Integer-Valued Time Series

This study considers the parameter change test for integer-valued time series models based on the Poisson quasi-maximum likelihood estimates. As a change point test, we consider the score vector-based CUSUM test and show that its limiting null distribution takes the form of a function of Brownian bridges. Moreover, the residual-based CUSUM tests are considered as alternatives. For evaluation, we conduct a Monte Carlo simulation study with Poisson, zero-inflated Poisson, negative binomial and Conway-Maxwell integer-valued generalized autoregressive conditional heteroscedastic models andPoisson integer-valued autoregressive models, and compare the performance of the proposed CUSUM tests. Our findings confirm that the proposed test is a functional tool for detecting a change point when the underlying distribution is unspecified.

Analysis of the occurrence, robustness and characteristics of abrupt changes in streamflow time series under future climate change

Understanding and quantifying the effects of future climate change is currently one of the most pressing challenges in science and of high relevance for society. Most future climate change studies consider changes between arbitrary time periods. We specify these time periods by splitting climate-change impacted streamflow time series at instances of highest change, by using statistical tests. We used the daily streamflow from 2000 to 2099 simulated from a comprehensive ensemble of the EURO-CORDEX climate change data in three basins across Germany (Treene, lowland; Kinzig, mid-range mountain; and Ammer, pre-alpine). Change points in each basin were detected by using six change point tests. The robustness of changes was analyzed with a bootstrapping procedure. A set of 32 Indicators of Hydrologic Alteration (IHA) was used to examine characteristics of hydrologic changes in the simulated discharge time series between pre- and post-change-point period in absolute change and in deviation of the Range of Variability Approach (RVA). The results show that the occurrence of change points due to climate change is spread throughout the decades, but strongly clustered in the current and upcoming decade. The selection of global and regional climate models impacts the occurrence of change points to a greater extent than the choice of greenhouse gas emission scenarios and bias correction method. The highest significant alteration of IHA occurs in the lowland-, less in the alpine- and least in the mid-range mountain catchment. The transition of hydrologic regimes to an alternative state after the identified change points is likely to occur because the majority of indicators move out of the current state of RVA. We further notice ecoregion-dependent changes in summer discharges and extreme low flows, which increase in the lowland and decrease in the pre-alpine catchment. This may have a detrimental effect on local aquatic communities. We conclude that the combined analysis of simulated climate scenarios, change points and IHA enables a better interpretability of potential future hydrological changes both in timing and severity and provides an early warning signal of changes for climate change mitigation.

The relationship between herding behavior and firm size before and after the elimination of short-sale price restrictions

The present paper investigates the relationship between investor herding behavior and stock return under short-sale price restrictions. Detailed intra-day orders are applied to calculate herding measurements before and after a staged lifting of short-sale restrictions on May 16th, 2005 and September 23rd, 2013 in Taiwan. The former targeted the constituent stocks of the Taiwan 50 Index only, while the latter targeted all listed firms on the Taiwan Stock Exchange. Using the Chow test and the dynamic structural change point test to confirm the effect of ending these restrictions, the results found that short-sale restrictions increased individual herding behavior in the context of the stocks of small firms, especially those stocks in the low quantile of stock returns. Conversely, herding behavior was not shown to significantly impact the stock returns of large firms either before or after the end of short-sale price constraints for either individual or institutional investors.

Analyzing the Impacts of Climate Variability and Land Surface Changes on the Annual Water–Energy Balance in the Weihe River Basin of China

The serious soil erosion problems and decreased runoff of the Loess Plateau may aggravate the shortage of its local water resources. Understanding the spatiotemporal influences on runoff changes is important for water resource management. Here, we study this in the largest tributary of the Yellow River, the Weihe River Basin. Data from four hydrological stations (Lin Jia Cun (LJC), Xian Yang (XY), Lin Tong (LT), and Hua Xian (HX)) and 10 meteorological stations from 1961–2014 were used to analyze changes in annual runoff. The Mann–Kendall test and Pettitt abrupt change point test diagnosed variations in runoff in the Weihe River basin; the time periods before and after abrupt change points are the base period (period I) and change period (period II), respectively. Within the Budyko framework, the catchment properties (ω in Fu’s equation) represent land surface changes; climate variability comprises precipitation (P) and potential evapotranspiration (ET0). All the stations showed a reduction in annual runoff during the recording period, of which 22.66% to 50.42% was accounted for by land surface change and 1.97% to 53.32% by climate variability. In the Weihe River basin, land surface changes drive runoff variation in LT and climate variability drives it in LJC, XY, and HX. The contribution of land surface changes to runoff reduction in period I was less than that in period II, indicating that changes in human activity further decreased runoff. Therefore, this study offers a scientific basis for understanding runoff trends and driving forces, providing an important reference for social development, ecological construction, and water resource management.

Towards an improved understanding of hydrological change – linking hydrologic metrics and multiple change point tests

Abstract Understanding the connections between climate, anthropogenic impacts, and hydrology is fundamental for assessing future climate change. However, a comprehensive methodology is lacking to understand significant changes in the discharge regime and their causes. We propose an approach that links change point tests with hydrologic metrics applied to two Vietnamese catchments where both climatic and anthropogenic changes are observed. The change points in discharge series are revealed by six widely used change point tests. Then, 171 hydrologic metrics are investigated to evaluate all possible hydrological changes that occurred between the pre- and post-change point period. The tests showed sufficient capabilities to detect hydrological changes caused by precipitation alterations and damming. Linking the change point tests to the hydrological metrics had three benefits: (1) the significance of each detected change point was evaluated, (2) we found which test responds to which hydrologic metric, and (3) we were able to disentangle the hydrological impacts of the climatic and anthropogenic changes. Due to its objectivity, the presented method can improve the interpretation of anthropogenic changes and climate change impacts on the hydrological system.

Nonparametric change point detection in multivariate piecewise stationary time series

ABSTRACTDetecting change points in multivariate time series is an important problem with numerous applications. We develop a nonparametric method to detect multiple change points in multivariate piecewise stationary processes when the locations and number of change points are unknown. Based on a test statistic that measures differences in the spectral density matrices through the norm, we sequentially identify points of local maxima in the test statistic and test for the significance of each of them being change points. In addition, the components responsible for the change in the covariance structure at each detected change point are identified. The asymptotic properties of the test for significant change points under the null and alternative hypothesis are derived. We illustrate the better performance of our method in comparison to some of the recent methods through a few simulation examples and discuss applications of our method in seismology and finance.

Testing for change points in censored quantile regression models

We develop a new method to test structural changes in quantile regression in the presence of fixed censoring. The testing procedure is based on the observations in an informative subsetand is conducted with the subgradient of the quantile objective function, which only requires estimating the model under the null hypothesis. The proposed method is easy to understand and convenient to compute.We establish the limiting distribution of the test statistic under the null hypothesis,and show that its asymptotic critical values can be obtained via simulation methods.Simulation studies show that the proposed method has competitive performance but higher computational efficiency compared with the Powell-based method in finite samples.In addition, an empirical application to the American earnings gap is used to illustrate the performance of the proposed method.

Hazard Assessment under Multivariate Distributional Change-Points: Guidelines and a Flood Case Study

One of the ultimate goals of hydrological studies is to assess whether or not the dynamics of the variables of interest are changing. For this purpose, specific statistics are usually adopted: e.g., overall indices, averages, variances, correlations, root-mean-square differences, monthly/annual averages, seasonal patterns, maximum and minimum values, quantiles, trends, etc. In this work, a distributional multivariate approach to the problem is outlined, also accounting for the fact that the variables of interest are often dependent. Here, the Copula Theory, the Failure Probabilities, and suitable non-parametric statistical Change-Point tests are used in order to provide an assessment of the hazard. A hydrological case study is utilized to illustrate the issue and the methodology (viz., assessment of a dam spillway), considering the bivariate dynamics of annual maximum flood peak and volume observed at the Ceppo Morelli dam (located in the Piedmont region, Northern Italy) over a 50-year period. In particular, several problems—often present in hydrological analyses—are debated: namely, (i) the uncertainties due to the presence of heavy tailed random variables, and (ii) the hydrological meaning/interpretation of the results of statistical tests. Furthermore, the suitability of the procedures proposed to fulfill the goals of the study (viz., detecting and interpreting non-stationarity) is discussed. Overall, the main recommendation is that statistical (multivariate) investigations may represent a necessary step, though they may not be sufficient to assess hydrological (environmental) hazards.

Modified tests for change points in variance in the possible presence of mean breaks

ABSTRACTThis paper considers the detection problem of variance changes for the time series involving abrupt and/or smooth breaks in mean. Often, in these situations, the tests of choice are based on cumulative sum of squares statistics. We show that the test statistics are not robust in the presence of broken mean and their sizes suffer severe distortions. The adjusted residual-based method is then proposed to eliminate these deficiencies and makes a significant improvement. Finally, simulation results confirm the validity of these modified test statistics, and an empirical data analysis using some stock price series from the Shanghai Stock Exchange is reported.