Positions Of Change-points Research Articles

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.

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.

Micro–Macro Changepoint Inference for Periodic Data Sequences

Existing changepoint approaches consider changepoints to occur linearly in time; one changepoint happens after another and they are not linked. However, data processes may have regularly occurring changepoints, for example, a yearly increase in sales of ice-cream on the first hot weekend. Using linear changepoint approaches here will miss more global features such as a decrease in sales of ice-cream due to other product availability. Being able to tease these global changepoint features from the more local (periodic) ones is beneficial for inference. We propose a periodic changepoint model to model this behavior using a mixture of a periodic and linear time perspective. Built around a Reversible Jump Markov chain Monte Carlo sampler, the Bayesian framework is used to study the local (periodic) changepoint behavior. To identify the optimal global changepoint positions we integrate the local changepoint model into the pruned exact linear time (PELT) search algorithm. We demonstrate that the method detects both local and global changepoints with high accuracy on simulated and motivating applications that share periodic behavior. Due to the micro–macro nature of the analysis, visualization of the results can be challenging. We additionally provide a unique perspective for changepoint visualizations in these data sequences. Supplementary Materials for this article are available online.

Multivariate change point detection for heterogeneous series

The multivariate change point detection problem has been encountered across various fields. Most approaches to this problem assume the series is homogeneous, i.e., all the coordinates change concurrently. Hence, the specific subset of the coordinates containing the change points cannot be determined. In this work, we propose S-MCPD, which is capable of detecting the position of multivariate change points for heterogeneous series by identifying specific coordinates of those changed. Specifically, the problem is discussed in the context of variable selection and transformed into the form of sparse group lasso. In simulation studies, we compared S-MCPD with four existing methods, inspect, sbs, dc, and cpm. The results showed that the performance of S-MCPD was comparable to that of inspect and was superior to other methods in terms of evaluation metrics. In addition, S-MCPD can determine not only the positions of change points, but also the subset of coordinates containing the change points, while other existing methods are unable to achieve this. Moreover, S-MCPD does not depend on the constant variance assumption and works quite well even when the covariance changes, which makes our method more practical. These are the two important contributions of our work. Finally, we applied S-MCPD to two real-world datasets to show its effectiveness.

Abnormal data cleaning of wind turbine power curve using Bayesian change point-quartile combined algorithm

During the operation of wind turbines, there are a lot of abnormal data collected from wind power data, which cannot be used to truly evaluate the performance and operation state of wind turbines. According to the distribution characteristics of these abnormal data, an outlier delete method using Bayesian change point-quartile combined algorithm is proposed. Firstly, to identify and delete the abnormal data below wind power curve, based on the Bayesian theorem, change point position is identified. Finally, the quartile method is utilized to delete the upper sparse outliers. The proposed method is applied to 10-min field monitoring wind power data, root mean square error (RMSE), program running time and the rejection rate of field wind turbine data are used to measure model accuracy, the results show that compared with the least squares (LS) change point method, the method proposed in this paper is feasible and effective.

GNSSseg, a Statistical Method for the Segmentation of Daily GNSS IWV Time Series

Homogenization is an important and crucial step to improve the usage of observational data for climate analysis. This work is motivated by the analysis of long series of GNSS Integrated Water Vapour (IWV) data, which have not yet been used in this context. This paper proposes a novel segmentation method called segfunc that integrates a periodic bias and a heterogeneous, monthly varying, variance. The method consists in estimating first the variance using a robust estimator and then estimating the segmentation and periodic bias iteratively. This strategy allows for the use of the dynamic programming algorithm, which is the most efficient exact algorithm to estimate the change point positions. The performance of the method is assessed through numerical simulation experiments. It is implemented in the R package GNSSseg, which is available on the CRAN. This paper presents the application of the method to a real data set from a global network of 120 GNSS stations. A hit rate of 32% is achieved with respect to available metadata. The final segmentation is made in a semi-automatic way, where the change points detected by three different penalty criteria are manually selected. In this case, the hit rate reaches 60% with respect to the metadata.

Comparative Analysis of Change-Point Techniques for Nonlinear Photovoltaic Performance Degradation Rate Estimations

A linear performance drop is generally assumed during the photovoltaic (PV) lifetime. However, operational data demonstrate that the PV module degradation rate ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Rd</i> ) is often nonlinear, which, if neglected, may increase the financial uncertainty. Although nonlinear behavior has been the subject of numerous publications, it was only recently that statistical models able to detect change-points and extract multiple <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Rd</i> values from PV performance time-series were introduced. A comparative analysis of six open-source libraries, which can detect change-points and calculate nonlinear <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Rd</i> , is presented in this article. Since the real <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Rd</i> and change-point locations are unknown in field data, 960 synthetic datasets from six locations and two PV module technologies have been generated using different aggregation and normalization decisions and nonlinear degradation rate patterns. The results demonstrated that coarser temporal aggregation (i.e., monthly vs. weekly), temperature correction, and both PV module technologies and climates with lower seasonality can benefit the change-point detection and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Rd</i> extraction. This also raises a concern that statistical models typically deployed for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Rd</i> analysis may be highly climatic- and technology-dependent. The comparative analysis of the six approaches demonstrated <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">median</i> mean absolute errors (MAE) ranging from 0.06 to 0.26%/year, given a maximum absolute <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Rd</i> of 2.9%/year. The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">median</i> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MAE</i> in change-point position detection varied from 3.5 months to 6 years.

Bayesian Change Point Estimation Based on Masked Data in Exponential Distribution Parallel System

Change point reflects a qualitative change in things. It has gained some applications in the field of reliability. In order to estimate the position parameters of the change point, a Bayesian change point model based on masked data and Gibbs sampling was proposed. By filling in missing lifetime data and introducing latent variables, the simple likelihood function is obtained for exponential distribution parallel system under censored data. This paper describes the probability distributions and random generation methods of the missing lifetime variables and latent variables, and obtains the full conditional distributions of the change point position parameters and other unknown parameters. By Gibbs sampling and estimation of unknown parameters, the estimates of the mean, median, and quantile of the parameter posterior distribution are obtained. The specific steps of Gibbs sampling are introduced in detail. The convergence of Gibbs sampling is also diagnosed. Random simulation results show that the estimations are fairly accurate.

Estimating piecewise monotone signals

We study the problem of estimating piecewise monotone vectors. This problem can be seen as a generalization of the isotonic regression that allows a small number of order-violating changepoints. We focus mainly on the performance of the nearly-isotonic regression proposed by Tibshirani et al. (2011). We derive risk bounds for the nearly-isotonic regression estimators that are adaptive to piecewise monotone signals. The estimator achieves a near minimax convergence rate over certain classes of piecewise monotone signals under a weak assumption. Furthermore, we present an algorithm that can be applied to the nearly-isotonic type estimators on general weighted graphs. The simulation results suggest that the nearly-isotonic regression performs as well as the ideal estimator that knows the true positions of changepoints.

Bayesian Detection of Piecewise Linear Trends in Replicated Time-Series with Application to Growth Data Modelling.

We consider the situation where a temporal process is composed of contiguous segments with differing slopes and replicated noise-corrupted time series measurements are observed. The unknown mean of the data generating process is modelled as a piecewise linear function of time with an unknown number of change-points. We develop a Bayesian approach to infer the joint posterior distribution of the number and position of change-points as well as the unknown mean parameters. A-priori, the proposed model uses an overfitting number of mean parameters but, conditionally on a set of change-points, only a subset of them influences the likelihood. An exponentially decreasing prior distribution on the number of change-points gives rise to a posterior distribution concentrating on sparse representations of the underlying sequence. A Metropolis-Hastings Markov chain Monte Carlo (MCMC) sampler is constructed for approximating the posterior distribution. Our method is benchmarked using simulated data and is applied to uncover differences in the dynamics of fungal growth from imaging time course data collected from different strains. The source code is available on CRAN.

Change points, memory and epidemic spreading in temporal networks

Dynamic networks exhibit temporal patterns that vary across different time scales, all of which can potentially affect processes that take place on the network. However, most data-driven approaches used to model time-varying networks attempt to capture only a single characteristic time scale in isolation — typically associated with the short-time memory of a Markov chain or with long-time abrupt changes caused by external or systemic events. Here we propose a unified approach to model both aspects simultaneously, detecting short and long-time behaviors of temporal networks. We do so by developing an arbitrary-order mixed Markov model with change points, and using a nonparametric Bayesian formulation that allows the Markov order and the position of change points to be determined from data without overfitting. In addition, we evaluate the quality of the multiscale model in its capacity to reproduce the spreading of epidemics on the temporal network, and we show that describing multiple time scales simultaneously has a synergistic effect, where statistically significant features are uncovered that otherwise would remain hidden by treating each time scale independently.

Computationally Efficient Off-Line Joint Change Point Detection in Multiple Time Series

In this paper, a computationally efficient algorithm for Bayesian joint change point detection (CPD) in multiple time series is presented. The data generation model includes a number of change configurations (CC), each affecting a unique subset of the time series, which introduces correlation between the positions of change points (CPs) in the monitored time series. The inference objective is to identify joint changes and the associated CC. The algorithm consists of two stages: First, a univariate CPD algorithm is applied separately to each of the involved time series. The outcomes of this step are maximum <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a posteriori</i> (MAP) detected CPs and posterior distributions of CPs conditioned on the MAP CPs. These outcomes are used in combination to approximate the posterior for the CCs. In the second algorithm stage, dynamic programming is used to find the maxima of this approximate CC posterior. The algorithm is applied to synthetic data, and it is shown to be both significantly faster and more accurate compared to a previously proposed algorithm designed to solve similar problems. Also, the initial algorithm is extended with steps from the maximization–maximization algorithm, which allows the hyperparameters of the data generation model to be estimated jointly with the CCs, and we show that these estimates coincide with estimates obtained from a Markov chain Monte Carlo algorithm.

Fourier methods for analyzing piecewise constant volatilities

We develop procedures for testing whether a sequence of independent random variables has constant variance. If this is fulfilled, the modulus of a Fourier-type transformation of the volatility process is identically equal to one. Our approach takes advantage of this property considering a canonical estimator for the modulus under the assumption of piecewise identically distributed zero mean observations. Using blockwise variance estimation, we introduce several test statistics resulting from different weight functions. All of them are given by simple explicit formulae. We prove the consistency of the corresponding tests and compare them to alternative procedures on extensive Monte Carlo experiments. According to the results, our proposals offer fairly high power, particularly in the case of multiple structural breaks. They also allow for an adequate estimation of the change point positions. We apply our procedure to gold mining data and also briefly discuss how it can be modified to test for the stationarity of other distributional parameters.

On high-dimensional change point problem

New statistics are proposed to estimate and test the structural change when the data dimension is comparable to or larger than the sample size. Consistency of the new statistic in estimating the change point position is established under the alternative hypothesis. The asymptotic distribution of the new statistic in testing the existence of a change point is obtained under the null hypothesis. Some simulation results are presented which show that the numerical performance of our method is satisfactory. The method is illustrated via the analysis of the house price index of US.

Stochastic approximation Monte Carlo EM for change-point analysis

ABSTRACTIn the expectation–maximization (EM) algorithm for maximum likelihood estimation from incomplete data, Markov chain Monte Carlo (MCMC) methods have been used in change-point inference for a long time when the expectation step is intractable. However, the conventional MCMC algorithms tend to get trapped in local mode in simulating from the posterior distribution of change points. To overcome this problem, in this paper we propose a stochastic approximation Monte Carlo version of EM (SAMCEM), which is a combination of adaptive Markov chain Monte Carlo and EM utilizing a maximum likelihood method. SAMCEM is compared with the stochastic approximation version of EM and reversible jump Markov chain Monte Carlo version of EM on simulated and real datasets. The numerical results indicate that SAMCEM can outperform among the three methods by producing much more accurate parameter estimates and the ability to achieve change-point positions and estimates simultaneously.

A changepoint analysis of spatio-temporal point processes

This work introduces a Bayesian approach to detecting multiple unknown changepoints over time in the inhomogeneous intensity of a spatio-temporal point process with spatial and temporal dependence within segments. We propose a new method for detecting changes by fitting a spatio-temporal log-Gaussian Cox process model using the computational efficiency and flexibility of integrated nested Laplace approximation, and by studying the posterior distribution of the potential changepoint positions. In this paper, the context of the problem and the research questions are introduced, then the methodology is presented and discussed in detail. A simulation study assesses the validity and properties of the proposed methods. Lastly, questions are addressed concerning potential unknown changepoints in the intensity of radioactive particles found on Sandside beach, Dounreay, Scotland.

Detecting multiple structural breaks on a Koyck distributed lag model: A Bayesian approach

Koyck Distributed Lag Model undergoing a possible multiple structural changes occurring at unknown positions in time is analyzed using Bayesian approach. The posterior distribution of the number of change points and the positions of the structural change points are derived using filtering recursions similar to forward-backward algorithms. The segments are assumed to be independent, and so are the priors. Normal and gamma priors are used for lag weights and variance, respectively. The priors used for number of change points and position of change points are binomial and uniform discrete distributions, respectively. Only the parameter β’s (lag weights) are allowed to change.

Mutil-Conditions Impress Nonsingular Dimensional Cellular Automaton on Traffic Flow

This paper is based on Nagel-Schreckenberg cellular automata model as the foundation, in the open boundary conditions, the traffic vehicle redirecting probability and before lane changing rules get to intersection will produce certain effect to interference with intersection , and so as to builds up the nonsingular cellular automata model. Through the research to redirecting probability, lane changing rules and the settings of traffic lights play a part in traffic flow characteristics, and points out the influence of phase change point position ,and at the same time, traffic lights timing differences can reduce vehicle interference to increase traffic flow, at the same time, play a analysis the critical redirecting probability of traffic flow in controlling significance, and points out the relationship between the critical point of Lane changing probability and traffic flow influence ,and lane-changing rules is correspond to the basic line of vehicles running.

Segmentation uncertainty in multiple change-point models

This paper addresses the retrospective or off-line multiple change-point detection problem. In this context, there is a need of efficient diagnostic tools that enable to localize the segmentation uncertainty along the observed sequence. Concerning the segmentation uncertainty, the focus was mainly on the change-point position uncertainty. We propose to state this problem in a new way, viewing multiple change-point models as latent structure models and using results from information theory. This led us to show that the segmentation uncertainty is not reflected in the posterior distributions of the change-point position because of the marginalization that is intrinsic in the computation of these posterior distributions. The entropy of the segmentation of a given observed sequence can be considered as the canonical measure of segmentation uncertainty. This segmentation entropy can be decomposed as conditional entropy profiles that enables to localize this canonical segmentation uncertainty along the sequence. One of the main outcomes of this work is to derive efficient algorithms to compute these conditional entropy profiles. The proposed approach benefits from all the properties of the Shannon---Khinchin axioms of entropy and therefore is the unique approach for localizing the canonical segmentation uncertainty along the sequence. We introduce the Kullback---Leibler divergence of the uniform distribution from the segmentation distribution for successive numbers of change points as a new tool for assessing the number of change points selected by different methods. The proposed approach is illustrated using four contrasted examples.

Bayesian Time Series Analysis of Structural Changes in Level and Trend

In this article we consider the problem of detecting changes in level and trend in time series model in which the number of change-points is unknown. The approach of Bayesian stochastic search model selection is introduced to detect the configuration of changes in a time series. The number and positions of change-points are determined by a sequence of change-dependent parameters. The sequence is estimated by its posterior distribution via the maximum a posteriori (MAP) estimation. Markov chain Monte Carlo (MCMC) method is used to estimate posterior distributions of parameters. Some actual data examples including a time series of traffic accidents and two hydrological time series are analyzed.