Location Of Change Points Research Articles

Change point detection in INAR(p) models via likelihood ratio scanning method

In this paper, we consider an integer-valued autoregressive (INAR) model. Based on the likelihood ratio scanning method (LRSM), the numbers and locations of the piecewise stationary INAR process change points are discussed. The minimum description length (MDL) function of the INAR model is given. Moreover, we also study the case when the sum of coefficients in each segment of the model tends to 1 and make adjustments to the MDL criterion in the LRSM. In this way, the accuracy of change point detection is improved. In the end, simulation experiments and real data analysis are conducted to illustrate the efficiency of the LRSM.

Multiscale Change Point Detection for Univariate Time Series Data with Missing Value

This paper studies the autoregressive integrated moving average (ARIMA) state space model combined with Kalman smoothing to impute missing values in a univariate time series before detecting change points. We estimate a scale-dependent time-average variance constant that depends on the length of the data section and is robust to mean shifts under serial dependence. The consistency of the proposed estimator is shown under the assumption allowing heavy tailedness. Integrating the proposed estimator with the moving sum and wild binary segmentation procedures to determine the number and locations of change points is discussed. Furthermore, the performance of the proposed methods is evaluated through extensive simulation studies and applied to the Beijing multi-site air quality dataset to impute missing values and detect mean changes in the data.

Changes in Climatological Variables at Stations around Lake Erie and Lake Michigan

Climatological variables undergo changes over time, and it is important to understand such dynamic changes at global, regional, and local levels. While global and regional studies are common in the study of climate, such studies at a local level are not as common. The aim of this article is to study temporal changes in precipitation, snowfall, and temperature variables at specific stations located on the rims of Lake Erie and Lake Michigan. The identification of changes is carried out by applying change-point analysis to precipitation, snowfall, and temperature data from Buffalo, Erie, and Cleveland stations located on the rim of Lake Erie and at Chicago, Milwaukee, and Green Bay stations located on the rim of Lake Michigan. We adopt mainly the Bayesian information criterion (BIC) method to identify the number and locations of change points, and then we apply the generalized likelihood ratio statistic to test for the statistical significance of the identified change points. We follow this up by finding 95% confidence intervals for those change points that were found to be statistically significant. The results from the analysis show that there are significant changes in precipitation, snowfall, and temperature variables at all six rim stations. Changes in precipitation show consistently significant increases, whereas there is no similar consistency in snowfall increases. Temperature increases are generally quite sharp, and they occur consistently around 1985. Overall, upon combining the amounts of changes from all six stations, the average amount of change in annual average temperature is found to be 0.96 °C, the average percentage of change in precipitation is 16%, and the average percentage of change in snowfall is 17%. The changing local climatic conditions identified in the study are important for local city planners, as well as residents, so that they can be well prepared for changing climatic scenarios.

Bayesian multiple change-points detection in autocorrelated binary process with application to COVID-19 infection pattern

Maintaining consistent model parameters in long-run experiments is challenging. We study the multiple change-points detection problem from this viewpoint for an autocorrelated sample path of a binary response variable. The probabilities of success and correlation structure are linked to explanatory or control variables using a generalized linear model. A Bayesian paradigm is introduced here to estimate the unknown number and locations of change-points and an adaptive RJMCMC algorithm is presented to generate pseudo-random samples from the posterior distributions. This approach allows researchers to incorporate the experts' ideas into the analysis of such data. The features of the proposed method are examined via some simulation studies. We also apply the presented method to COVID-19 data from four countries to detect the change-points in the infection procedures in the presence of some explanatory variables.

A Distribution-Free Method for Change Point Detection in Non-Sparse High Dimensional Data

We propose a distribution-free distance-based method for high dimensional change points that can address challenging situations when the sample size is very small compared to the dimension as in the so-called HDLSS data or when non-sparse changes may occur due to change in many variables but with small significant magnitudes. Our method can detect changes in mean or variance of high dimensional observations as well as other distributional changes. We present efficient algorithms that can detect single and multiple high dimensional change points. We use nonparametric metrics, including a new dissimilarity measure and some new distance and difference distance matrices, to develop a procedure to estimate change point locations. We also introduce a nonparametric test to determine the significance of estimated change points. We provide theoretical guaranties for our method and demonstrate its empirical performance in comparison with some of the recent methods for high dimensional change points. An R package called HDDchangepoint is developed to implement the proposed method.

Generalized fiducial inference for the GEV change-point model

Generalized extreme value (GEV) distribution is used to analyse the maximum from a block of data. It is very useful to describe the unusual event rather than the usual event. In this paper, we propose a change-point detection procedure for GEV distribution based on generalized fiducial inference. The fiducial distribution of the change-point location is constructed. Meanwhile, Markov Chain Monte Carlo method combined with Gibbs sampling and the Metropolis–Hastings algorithm is utilised to estimate the location of the change point and its confidence interval. In addition, the generalized fiducial factor is used to test whether there is a change point. Simulation results show that the proposed generalized fiducial method performs better in accuracy, robustness and the length of confidence intervals. Finally, we apply the proposed method to the annual maximum rainfall data in Beijing.

Reliability analysis of inverse Gaussian processes with two-stage degenerate paths

For randomly degraded products undergoing a two-stage degradation process, traditional random effects models assume that the degradation rate follows a symmetrically normal distribution. However, certain products exhibit asymmetric degradation rates. In light of this, this paper proposes an approach for reliability analysis based on the inverse Gaussian (IG) degeneration process, which considers both asymmetric random effects and the two-stage nature simultaneously. To begin with, we establish a two-stage IG degradation process model that incorporates a skew normal random effect. Subsequently, we determine the location of change points using the Schwarz Information Criterion (SIC). The estimation of parameters is then conducted by combining Maximum Likelihood Estimations (MLEs) with the Genetic Algorithm (GA). Finally, we validate and demonstrate the practicality for the proposed model through Monte Carlo (MC) simulation and examples involving lithium batteries.

Change Point Test for Length-Biased Lognormal Distribution under Random Right Censoring

The length-biased lognormal distribution is a length-biased version of lognormal distribution, which is developed to model the length-biased lifetime data from, for example, biological investigation, medical research, and engineering fields. Owing to the existence of censoring phenomena in lifetime data, we study the change-point-testing problem of length-biased lognormal distribution under random censoring in this paper. A procedure based on the modified information criterion is developed to detect changes in parameters of this distribution. Under the sufficient condition of the Fisher information matrix being positive definite, it is proven that the null asymptotic distribution of the test statistic follows a chi-square distribution. In order to evaluate the uncertainty of change point location estimation, a way of calculating the coverage probabilities and average lengths of confidence sets of change point location based on the profile likelihood and deviation function is proposed. The simulations are conducted, under the scenarios of uniform censoring and exponential censoring, to investigate the validity of the proposed method. And the results indicate that the proposed approach performs better in terms of test power, coverage probabilities, and average lengths of confidence sets compared to the method based on the likelihood ratio test. Subsequently, the proposed approach is applied to the analysis of survival data from heart transplant patients, and the results show that there are differences in the median survival time post-heart transplantation among patients of different ages.

A novel dual-criterion framework for change point detection

In this work, we introduce a dual-criterion framework for change-point detection. This innovative approach intuitively facilitates the simultaneous determination of both the number and locations of change points, while effectively identifying and excluding outliers. Numerous one-dimensional criterion-based change point detection methods can be generalized and integrated within this novel framework.

A constant-per-iteration likelihood ratio test for online changepoint detection for exponential family models

Online changepoint detection algorithms that are based on (generalised) likelihood-ratio tests have been shown to have excellent statistical properties. However, a simple online implementation is computationally infeasible as, at time T, it involves considering O(T) possible locations for the change. Recently, the FOCuS algorithm has been introduced for detecting changes in mean in Gaussian data that decreases the per-iteration cost to O(logT)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(\\log T)$$\\end{document}. This is possible by using pruning ideas, which reduce the set of changepoint locations that need to be considered at time T to approximately logT\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\log T$$\\end{document}. We show that if one wishes to perform the likelihood ratio test for a different one-parameter exponential family model, then exactly the same pruning rule can be used, and again one need only consider approximately logT\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\log T$$\\end{document} locations at iteration T. Furthermore, we show how we can adaptively perform the maximisation step of the algorithm so that we need only maximise the test statistic over a small subset of these possible locations. Empirical results show that the resulting online algorithm, which can detect changes under a wide range of models, has a constant-per-iteration cost on average.

Joint Random Partition Models for Multivariate Change Point Analysis

Change point analyses are concerned with identifying positions of an ordered stochastic process that undergo abrupt local changes of some underlying distribution. When multiple processes are observed, it is often the case that information regarding the change point positions is shared across the different processes. This work describes a method that takes advantage of this type of information. Since the number and position of change points can be described through a partition with contiguous clusters, our approach develops a joint model for these types of partitions. We describe computational strategies associated with our approach and illustrate improved performance in detecting change points through a small simulation study. We then apply our method to a financial data set of emerging markets in Latin America and highlight interesting insights discovered due to the correlation between change point locations among these economies.

TIME SERIES WITH MULTIPLE CHANGE POINTS AND CENSORED OBSERVATIONS

This article examines a Bayesian model for a nonstationary time series with an unknown number of change points and censored observations. Each segment is assumed to be an autoregressive process with order one. To estimate the number and locations of change points, we use the reversible jump Markov chain Monte Carlo (RJMCMC) algorithm. The censored problem is solved by imputing the censored values from a multivariate normal distribution based on the observed part. A numerical example shows that the estimates of the number of change points and their localizations have little bias. Additionally, the estimates are robust to the censoring percentage.

A Composite Likelihood-based Approach for Change-point Detection in Spatio-temporal Processes

This paper develops a unified and computationally efficient method for change-point estimation along the time dimension in a non-stationary spatio-temporal process. By modeling a non-stationary spatio-temporal process as a piecewise stationary spatio-temporal process, we consider simultaneous estimation of the number and locations of change-points, and model parameters in each segment. A composite likelihood-based criterion is developed for change-point and parameter estimation. Under the framework of increasing domain asymptotics, theoretical results including consistency and distribution of the estimators are derived under mild conditions. In contrast to classical results in fixed dimensional time series that the localization error of change-point estimator is , exact recovery of true change-points is possible in the spatio-temporal setting. More surprisingly, the consistency of change-point estimation can be achieved without any penalty term in the criterion function. In addition, we further establish consistency of the change-point estimator under the infill asymptotics framework where the time domain is increasing while the spatial sampling domain is fixed. A computationally efficient pruned dynamic programming algorithm is developed for the challenging criterion optimization problem. Extensive simulation studies and an application to the U.S. precipitation data are provided to demonstrate the effectiveness and practicality of the proposed method.

Change-points analysis for generalized integer-valued autoregressive model via minimum description length principle

This article considers the problem of modeling a class of count time series with multiple change-points using segmented generalized integer-valued autoregressive (S-GINAR) processes. The minimum description length principle (MDL) is applied to study the statistical inference for the S-GINAR model, and the consistency results of the MDL model selection procedure are established respectively under the condition of known and unknown number of change-points. To find the “best” combination of the number of change-points, the locations of change-points, the order of each segment and its parameters, a genetic algorithm with simulated annealing is implemented to solve this difficult optimization problem. In particular, the simulated annealing process makes up for the precocious problem of the traditional genetic algorithm. Numerical results from simulation experiments and three examples of real data analysis show that the procedure has excellent empirical properties.

Multiple change-points estimation in panel data models via SaRa

Multiple change-points estimation in panel data models is one of the popular topics in statistics. In this article, we investigate the multiple change-points estimation in the mean of panel data model based on a screening and ranking algorithm. Firstly, the possible change-points are initially screened based on local statistics. Secondly, the threshold is used to further screen the change-points. Finally, the final change-points are screened out using the information criterion. Furthermore, the consistency of the change-point estimators is proved. The Monte Carlo simulation results show that the proposed method can estimate the number and locations of change-points accurately even if the error terms are serially correlated or cross-sectionally correlated, and finally the method is used to analyze the annual GDP growth rate data of 47 countries in the word from 1971 to 2019 to illustrate the effectiveness of the method.

Remaining useful life prediction using nonlinear multi-phase Wiener process and variational Bayesian approach

Due to the changeable internal mechanisms or external working conditions, the degradation trend of products usually presents multiple phase characteristics. However, most existing multi-phase degradation methods treat each phase as linear and rely on artificial designation to directly specify the forms of drift models, which may result in an inaccurate description of degradation characteristics for complex equipment. To this end, we formulate a general nonlinear multi-phase degradation model with three-source variability based on the Wiener process. Meanwhile, a stage division method is developed to automatically determine the degradation phase number, change-point locations, and the forms of drift models. Then, we obtain the expressions of remaining useful life (RUL) by considering the uncertainty of change-point degradation observations. Especially, we derive the approximate analytical solution of RUL based on the linear model. Furthermore, to fully consider the unit-to-unit heterogeneity and utilize the degradation observations of the in-service unit and prior information simultaneously, we propose a parameter estimation method based on variational Bayesian approach, which adaptively updates all parameters as random variables. Finally, two numerical examples and three practical examples are provided to verify the effectiveness of the proposed method.

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.

A change point-based analysis procedure for improving the success rate of decision-making in clinical trials with delayed treatment effects.

A delayed treatment effect is a commonly observed phenomenon in tumor immunotherapy clinical trials. It can cause a loss of statistical power and complicate the interpretation of the analytical findings. This phenomenon also poses challenges for interim analysis in the context of phase II/III seamless design or group sequential design. It shows potential to lead researchers to make incorrect go/no-go decisions. Despite its significance, rare research has explored the impact of delayed treatment effects on the decision success rate of the interim analysis and the methods to compensate for this loss. In this study, we propose an analysis procedure based on change points for improving the decision success rate at the interim analysis in the presence of delayed treatment effects. This procedure primarily involves three steps: I. detecting and testing the number and locations of change points; II. estimating treatment efficacy; and III. making go/no-go decisions. Simulation results demonstrate that when there is a delayed treatment effect with a single change point, using the proposed analysis procedure significantly improves the decision success rate while controlling the type I error rate. Moreover, the proposed method exhibits very little disparity compared to the unadjusted method when the proportional hazards assumption holds. Therefore, the proposed analysis procedure provides a feasible approach for decision-making at the interim analysis when delayed treatment effects are present.

Change point detection for high dimensional data via kernel measure with application to human aging brain data.

Identifying the existence and locations of change points has been a broadly encountered task in many statistical application areas. The existing change point detection methods may produce unsatisfactory results for high-dimensional data since certain distributional assumptions are made on data, which are hard to verify in practice. Moreover, some parameters (such as the number of change points) need to be estimated beforehand for some methods, making their powers sensitive to these values. Here, we propose a kernel-based -statistic to identify change points (KUCP) for high dimensional data, which is free of distributional assumptions and sup-parameter estimations. Specifically, we employ a kernel function to describe similarities among the subjects and construct a -statistic to test the existence of change point for a given location. The asymptotic properties of the -statistic are deduced. We also develop a procedure to locate the change points sequentially via a dichotomy algorithm. Extensive simulations demonstrate that KUCP has higher sensitivity in identifying existence of change points and higher accuracy in locating these change points than its counterparts. We further illustrate its practical utility by analyzing a gene expression data of human brain to detect the time point when gene expression profiles begin to change, which has been reported to be closely related with aging brain.

Modified information criterion for detecting changes in skew slash distribution

Abstract Skew slash distribution is a distribution which considers both skewness and heavy tail. It is very useful in simulation studies and realistic in representing practical data due to its less peaks, especially in data sets that violate the assumption of normality. In this article, we propose a change-point detection procedure for skew slash distribution based on the modified information criterion (MIC). Meanwhile, we provide an estimation approach based on confidence distribution (CD) to measure the accuracy of change point location estimation. By comparing with the likelihood ratio test, the simulation results show that the MIC-based method performs better in terms of powers, the coverage probabilities and average lengths of confidence sets. In the end, we apply our proposed method to real data and locate the positions of the change points successfully.