Change-point Problem Research Articles

Multiple change‐point detection for regression curves

AbstractNonparametric estimation of a regression curve becomes crucial when the underlying dependence structure between covariates and responses is not explicit. While existing literature has addressed single change‐point estimation for regression curves, the problem of multiple change points remains unresolved. In an effort to bridge this gap, this article introduces a nonparametric estimator for multiple change points by minimizing a penalized weighted sum of squared residuals, presenting consistent results under mild conditions. Additionally, we propose a cross‐validation‐based procedure that possesses the advantage of being tuning‐free. Our simulation results showcase the competitive performance of these new procedures when compared with state‐of‐the‐art methods. As an illustration of their utility, we apply these procedures to a real dataset.

Some clustering-based change-point detection methods applicable to high dimension, low sample size data

Detection of change-points in a sequence of high dimensional observations is a challenging problem, and this becomes even more challenging when the sample size (i.e., the sequence length) is small. In this article, we propose some change-point detection methods based on clustering, which can be conveniently used in such high dimension, low sample size situations. First, we consider the single change-point problem. Using k-means clustering based on a suitable dissimilarity measures, we propose some methods for testing the existence of a change-point and estimating its location. High dimensional behavior of these proposed methods are investigated under appropriate regularity conditions. Next, we extend our methods for detection of multiple change-points. We carry out extensive numerical studies and analyze a real data set to compare the performance of our proposed methods with some state-of-the-art methods.

Grouped Change-Points Detection and Estimation in Panel Data

The change-points in panel data can be obstacles for fitting models; thus, detecting change-points accurately before modeling is crucial. Extant methods often either assume that all panels share the common change-points or that grouped panels have the same unknown parameters. However, the problem of different change-points and model parameters between panels has not been solved. To deal with this problem, a novel approach is proposed here to simultaneously detect and estimate the grouped change-points precisely by employing an iterative algorithm and the penalty cost function. Some numerical experiments and case studies are utilized to demonstrate the superior performance of the proposed method in grouping the panels, and estimating the number and positions of change-points.

ОБНАРУЖЕНИЕ РАЗЛАДОК В НЕСТАЦИОНАРНЫХ РЯДАХ НАБЛЮДЕНИЙ: ОБЗОР ТЕХНОЛОГИЙ И КРИТИЧЕСКИЙ АНАЛИЗ

A critical analysis of modern mathematical technologies used to solve the problem of nonstationary time series change point, taking into account the chaotic nature of the observed processes, is considered. The known methods of the quickest change point detection in nonstationary time series described by traditional models of random processes are considered as initial assumptions. The discrepancy between the known time series observation models and the real processes occurring in unstable immersion environments described by the concept of stochastic chaos is shown. Time series segmentation technologies based on a posteriori analysis of changes in the properties of observation sites of chaotic processes are presented. Options for building online algorithms for the quickest change point detection based on methods of multiregressive data analysis and metric machine learning technologies are considered.

Empirical likelihood method for detecting change points in network autoregressive models

<p>The network autoregressive model is a super high-dimensional time series model that can fully explain social relationships. This model can fully reflect the complex relationships in reality. Therefore, it plays a vital role in detecting the inflection point problem of this network autoregressive model for economics and finance. In this paper, we proposed the change-point problem of detecting network autoregressive models using empirical likelihood statistics based on the expected error term of the switching rule being 0, using the empirical likelihood method. Moreover, the asymptotic null distribution of the proposed empirical likelihood statistic was investigated. Simulation studies based on different settings were considered, and the results showed that the power of test statistics is significant. In the end, the Chinese stock market was investigated to demonstrate the significance of the proposed method.</p>

An Advanced Segmentation Approach to Piecewise Regression Models

Two problems concerning detecting change-points in linear regression models are considered. One involves discontinuous jumps in a regression model and the other involves regression lines connected at unknown places. Significant literature has been developed for estimating piecewise regression models because of their broad range of applications. The segmented (SEG) regression method with an R package has been employed by many researchers since it is easy to use, converges fast, and produces sufficient estimates. The SEG method allows for multiple change-points but is restricted to continuous models. Such a restriction really limits the practical applications of SEG when it comes to discontinuous jumps encountered in real change-point problems very often. In this paper, we propose a piecewise regression model, allowing for discontinuous jumps, connected lines, or the occurrences of jumps and connected change-points in a single model. The proposed segmentation approach can derive the estimates of jump points, connected change-points, and regression parameters simultaneously, allowing for multiple change-points. The initializations of the proposed algorithm and the decision on the number of segments are discussed. Experimental results and comparisons demonstrate the effectiveness and superiority of the proposed method. Several real examples from diverse areas illustrate the practicability of the new method.

Good Practices and Common Pitfalls in Climate Time Series Changepoint Techniques: A Review

Abstract Climate changepoint (homogenization) methods abound today, with a myriad of techniques existing in both the climate and statistics literature. Unfortunately, the appropriate changepoint technique to use remains unclear to many. Further complicating issues, changepoint conclusions are not robust to perturbations in assumptions; for example, allowing for a trend or correlation in the series can drastically change changepoint conclusions. This paper is a review of the topic, with an emphasis on illuminating the models and techniques that allow the scientist to make reliable conclusions. Pitfalls to avoid are demonstrated via actual applications. The discourse begins by narrating the salient statistical features of most climate time series. Thereafter, single- and multiple-changepoint problems are considered. Several pitfalls are discussed en route and good practices are recommended. While most of our applications involve temperatures, a sea ice series is also considered. Significance Statement This paper reviews the methods used to identify and analyze the changepoints in climate data, with a focus on helping scientists make reliable conclusions. The paper discusses common mistakes and pitfalls to avoid in changepoint analysis and provides recommendations for best practices. The paper also provides examples of how these methods have been applied to temperature and sea ice data. The main goal of the paper is to provide guidance on how to effectively identify the changepoints in climate time series and homogenize the series.

On the Asymptotic Approach to the Change-Point Problem and Exponential Convergence Rate in the Ergodic Theorem for Markov Chains

On the Asymptotic Approach to the Change-Point Problem and Exponential Convergence Rate in the Ergodic Theorem for Markov Chains

Bayesian Analysis of Change Point Problems Using Conditionally Specified Priors

In data analysis, change point problems correspond to abrupt changes in stochastic mechanisms generating data. The detection of change points is a relevant problem in the analysis and prediction of time series. In this paper, we consider a class of conjugate prior distributions obtained from conditional specification methodology for solving this problem. We illustrate the application of such distributions in Bayesian change point detection analysis with Poisson processes. We obtain the posterior distribution of model parameters using general bivariate distribution with gamma conditionals. Simulation from the posterior are readily implemented using a Gibbs sampling algorithm. The Gibbs sampling is implemented even when using conditional densities that are incompatible or only compatible with an improper joint density. The application of such methods will be demonstrated using examples of simulated and real data.

Change point estimation in an [formula omitted] queue with heterogeneous servers

The change point problem in the inter-arrival time of an M/M/2 queue with heterogeneous servers is studied here. In this model, it is assumed that the queue is in a steady state and that customers are served by the fastest available server and that there is no transfer of customers between servers. Maximum likelihood estimators are deducted for the arrival rates after and before the change point and for the service rates. Monte Carlo simulation results are presented that attest to the effectiveness and efficiency of the deduced estimators.

On Bayesian Estimation in Change-point Problems for Poisson Source localization on the plane in non Standard Situation

On Bayesian Estimation in Change-point Problems for Poisson Source localization on the plane in non Standard Situation

A special issue on Bayesian inference: challenges, perspectives and prospects.

A special issue on Bayesian inference: challenges, perspectives and prospects.

Autocorrelation and Parameter Estimation in a Bayesian Change Point Model

A piecewise function can sometimes provide the best fit to a time series. The breaks in this function are called change points, which represent the point at which the statistical properties of the model change. Often, the exact placement of the change points is unknown, so an efficient algorithm is required to combat the combinatorial explosion in the number of potential solutions to the multiple change point problem. Bayesian solutions to the multiple change point problem can provide uncertainty estimates on both the number and location of change points in a dataset, but there has not yet been a systematic study to determine how the choice of hyperparameters or the presence of autocorrelation affects the inference made by the model. Here, we propose Bayesian model averaging as a way to address the uncertainty in the choice of hyperparameters and show how this approach highlights the most probable solution to the problem. Autocorrelation is addressed through a pre-whitening technique, which is shown to eliminate spurious change points that emerge due to a red noise process. However, pre-whitening a dataset tends to make true change points harder to detect. After an extensive simulation study, the model is applied to two climate applications: the Pacific Decadal Oscillation and a global surface temperature anomalies dataset.

Online change-point detection for a transient change

We consider a popular online change-point problem of detecting a transient change in distributions of i.i.d. random variables. For this change-point problem, several change-point procedures are formulated and some advanced results for a particular procedure are surveyed. Some new approximations for the average run length to false alarm are offered and the power of these procedures for detecting a transient change in mean of a sequence of normal random variables is compared.

Change point inference in ergodic diffusion processes based on high frequency data

We deal with the change point problem in ergodic diffusion processes based on high frequency data. Tonaki et al. [12,13] studied the change point problem for the ergodic diffusion process model. However, the change point problem for the drift parameter when the diffusion parameter changes is still open. Therefore, we consider the change detection and the change point estimation for the drift parameter taking into account that there is a change point in the diffusion parameter. Moreover, we examine the performance of the tests and the estimation with numerical simulations.

Robust multiscale estimation of time-average variance for time series segmentation

There exist several methods developed for the canonical change point problem of detecting multiple mean shifts, which search for changes over sections of the data at multiple scales. In such methods, estimation of the noise level is often required in order to distinguish genuine changes from random fluctuations due to the noise. When serial dependence is present, using a single estimator of the noise level may not be appropriate. Instead, it is proposed to adopt a scale-dependent time-average variance constant that depends on the length of the data section in consideration, to gauge the level of the noise therein. Accordingly, an estimator that is robust to the presence of multiple mean shifts is developed. The consistency of the proposed estimator is shown under general assumptions permitting heavy-tailedness, and its use with two widely adopted data segmentation algorithms, the moving sum and the wild binary segmentation procedures, is discussed. The performance of the proposed estimator is illustrated through extensive simulation studies and on applications to the house price index and air quality data sets.

Bayesian multiple changepoint detection with missing data and its application to the magnitude‐frequency distributions

AbstractThe detection of abrupt changes in an evolving pattern of time series in the presence of missing data still poses a challenge to real applications. We formulate the multiple changepoint problem into a latent Markov model on a countably infinite state space. For efficiency‐enhancing, we propose a partially collapsed Gibbs sampler for the inference of the joint posterior of the number of changepoints and their locations. Variants of Viterbi algorithms are suggested for obtaining the MAP estimates of random changepoints in the presence of missing data, which provides better performances in these varying‐dimensional problems. The method is generally applicable for multiple changepoint detection under a variety of missing data mechanism. The method is applied to a case study of the magnitude‐frequency distribution of the 2010 Darfield M7.1 earthquake sequence in New Zealand. We find out some unusual features of the seismic b‐value in the Darfield earthquake sequence. It is noted that two changepoints are detected and in contrast to the background seismic b‐value, relatively low b‐values in the early aftershock propagation period are identified. We suggest that this might be a forewarning of potentially devastatingly strong aftershocks. The advance in the method of b‐value changepoint detection will enhance our understanding of earthquake occurrence and potentially lead to improved risk forecasting.

Change-Point Detection and Regularization in Time Series Cross-Sectional Data Analysis

AbstractResearchers of time series cross-sectional data regularly face the change-point problem, which requires them to discern between significant parametric shifts that can be deemed structural changes and minor parametric shifts that must be considered noise. In this paper, we develop a general Bayesian method for change-point detection in high-dimensional data and present its application in the context of the fixed-effect model. Our proposed method, hidden Markov Bayesian bridge model, jointly estimates high-dimensional regime-specific parameters and hidden regime transitions in a unified way. We apply our method to Alvarez, Garrett, and Lange’s (1991, American Political Science Review 85, 539–556) study of the relationship between government partisanship and economic growth and Allee and Scalera’s (2012, International Organization 66, 243–276) study of membership effects in international organizations. In both applications, we found that the proposed method successfully identify substantively meaningful temporal heterogeneity in parameters of regression models.

Seeded binary segmentation: a general methodology for fast and optimal changepoint detection

Summary We propose seeded binary segmentation for large-scale changepoint detection problems. We construct a deterministic set of background intervals, called seeded intervals, in which single changepoint candidates are searched for. The final selection of changepoints based on these candidates can be done in various ways, adapted to the problem at hand. The method is thus easy to adapt to many changepoint problems, ranging from univariate to high dimensional. Compared to recently popular random background intervals, seeded intervals lead to reproducibility and much faster computations. For the univariate Gaussian change in mean set-up, the methodology is shown to be asymptotically minimax optimal when paired with appropriate selection criteria. We demonstrate near-linear runtimes and competitive finite sample estimation performance. Furthermore, we illustrate the versatility of our method in high-dimensional settings.

Information Approach for Change Point Analysis of EGGAPE Distribution and Application to COVID-19 Data

The exponentiated generalized Gull alpha power exponential distribution is an extension of the exponential distribution that can model data characterized by various shapes of the hazard function. However, change point problem has not been studied for this distribution. In this study, the change point detection of the parameters of the exponentiated generalized Gull alpha power exponential distribution is studied using the modified information criterion. In addition, the binary segmentation procedure is used to identify multiple change point locations. The assumption is that all the parameters of the EGGAPE distributions are considered changeable. Simulation study is conducted to illustrate the power of the modified information criterion in detecting change point in the parameters with different sample sizes. Three applications related to COVID-19 data are used to demonstrate the applicability of the MIC in detecting change point in real life scenario.