Change-point Estimation Research Articles

Estimating and Testing High Dimensional Factor Models With Multiple Structural Changes

This paper considers multiple changes in the factor loadings of a high dimensional factor model occurring at dates that are unknown but common to all subjects. Since the factors are unobservable, the problem is converted to estimating and testing structural changes in the second moments of the pseudo factors. We consider both joint and sequential estimation of the change points and show that the distance between the estimated and the true change points is Op(1). We find that the estimation error contained in the estimated pseudo factors has no effect on the asymptotic properties of the estimated change points as the cross-sectional dimension N and the time dimension T go to infinity jointly. No N-T ratio condition is needed. We also propose (i) tests for the null of no change versus the alternative of l changes (ii) tests for the null of l changes versus the alternative of l + 1 changes, and show that using estimated factors asymptotically has no effect on their limit distributions if √T/N→0. These tests allow us to make inference on the presence and number of structural changes. Simulation results show good performance of the proposed procedure. In an application to US quarterly macroeconomic data we detect two possible breaks.

An Integrative Analysis of Time-varying Regulatory Networks From High-dimensional Data.

Directed networks have been widely used to describe many biological processes and functions. Understanding the structure of biological networks, especially regulatory networks, could help discover the mechanisms underlying important biological processes and pathogenesis of diseases. Most network inference methods assume the network structure is time-invariant or stationary. However, in some processes, the network structure is non-stationary or time-varying. The stationary network inference methods might not be able to directly used to reconstruct time-varying networks. Some non-stationary network learning methods have been proposed to infer the networks, but, the inferred networks are not regulatory networks which require activation and inhibition information. This work proposes an integrative approach, which combines the changepoint estimation, weighted network learning and searching, and model checking technique, to reconstruct time varying regulatory networks from high-dimensional time series data. We illustrate this approach to study the structure changes of Drosophila's regulatory networks in its life cycle.

A new approach to optimal design of control charts based on change point estimation and total time on test plot

Estimation of the change point of a process may be the most important result and application of control charts in the literature of statistical process control. The time to the change point called process failure mechanism may have the most vital role in optimal design of control charts. Applying the total time on test plot as a supreme tool for the failure rate shape identification is proposed in this paper to pick out an appropriate failure model. The unknown parameters of the fitted distribution then can be estimated by some common statistical methods like maximum likelihood based on the estimated change point data. The generalized cost model of Rahim and Banerjee (1993) adapted for fitted shock model will determine eventually the optimal design parameters of control charts economically and statistically. A numerical study on the optimal design of -control chart illustrates our practical approach for production systems with bathtub-shaped failure rate.

Application of the bootstrap method for change points analysis in generalized linear models

In this paper, we focus on the construction methods of the prediction model, estimation methods of the change point locations, and the confidence intervals for the generalized linear model with piecewise different coefficients. As a standard approach for multiple change point analysis, the application of the hierarchical splitting algorithm is widely used. However, the hierarchical splitting algorithm has a high risk in that the standard error of the change point estimators become large and, therefore, the prediction accuracy of the estimated model decreases. To deal with this problem, we consider the application of a bootstrap method based on the hierarchical splitting algorithm. Through simulation studies, we compare the algorithms in terms of the prediction accuracy of the estimated model, bias and variance of the change point estimators, and the accuracy of the confidence intervals of the change points. From the result, we confirmed the utility of the bootstrap-based methods for change point analysis, especially the increased prediction accuracy of the obtained model, decreased standard error of the change point estimators, and construction of better confidence intervals depending on the situation. We also present the results of a simple example to demonstrate the utility of the method.

Change-point estimation for repairable systems combining bootstrap control charts and clustering analysis: Performance analysis and a case study

Change-point estimation for repairable systems combining bootstrap control charts and clustering analysis: Performance analysis and a case study

Non-parametric detection of atmospheric radon concentration anomalies related to earthquakes

Anomalous phenomena related to earthquakes have been studied to aid in the forecasting of large earthquakes. Radon (222Rn) concentration changes are known to be one of those phenomena. Many studies have quantified radon anomalies to identify physical aspects of radon emanations related to earthquakes. Here, we apply singular spectrum transformation, non-parametric analysis to estimate change points in time series, to atmospheric radon concentration. From 10 years of data from continuous observation of the atmospheric radon concentration over northeastern Japan and Hokkaido, we identify anomalies in the atmospheric radon concentration related to the moment releases of large earthquakes. Compared with a conventional model-based method, the singular spectrum transformation method identifies more anomalies. Moreover, we also find that change points in the atmospheric radon concentration prior to the 2011 Tohoku-Oki earthquake (Mw 9.0; 11 Mar. 2011, N38.1°, E142.9°) coincided with periods of other anomalous precursory phenomena. Our results indicate that singular spectrum transformation can be used to detect anomalies in atmospheric radon concentration related to the occurrences of large earthquakes.

Bayesian loss-based approach to change point analysis

A loss-based approach to change point analysis is proposed. In particular, the problem is looked from two perspectives. The first focuses on the definition of a prior when the number of change points is known a priori. The second contribution aims to estimate the number of change points by using a loss-based approach recently introduced in the literature. The latter considers change point estimation as a model selection exercise. The performance of the proposed approach is shown on simulated data and real data sets.

Estimating non-simultaneous changes in the mean of vectors

A sequence of independent vectors with correlated components is considered. It is supposed that there is one change point in the mean of each component and changes need not occur simultaneously. The asymptotic distribution of the change point estimators is studied. If the true change points are well separated, the explicit asymptotic distribution of the change point estimators is presented. In the case the true change points coincide, it is shown that the limit distribution of properly standardized change points estimates exists. It depends not only on the underlying time series dependence structure, but also on the ratio of the sizes of the changes. The asymptotic distribution function is not known, but due to the invariance principle it can be obtained by simulations.

Estimating dynamic brain functional networks using multi-subject fMRI data

A common assumption in the study of brain functional connectivity is that the brain network is stationary. However it is increasingly recognized that the brain organization is prone to variations across the scanning session, fueling the need for dynamic connectivity approaches. One of the main challenges in developing such approaches is that the frequency and change points for the brain organization are unknown, with these changes potentially occurring frequently during the scanning session. In order to provide greater power to detect rapid connectivity changes, we propose a fully automated two-stage approach which pools information across multiple subjects to estimate change points in functional connectivity, and subsequently estimates the brain networks within each state phase lying between consecutive change points. The number and positioning of the change points are unknown and learned from the data in the first stage, by modeling a time-dependent connectivity metric under a fused lasso approach. In the second stage, the brain functional network for each state phase is inferred via sparse inverse covariance matrices. We compare the performance of the method with existing dynamic connectivity approaches via extensive simulation studies, and apply the proposed approach to a saccade block task fMRI data.

The multiple filter test for change point detection in time series

A framework for the detection of change points in the expectation in sequences of random variables is presented. Specifically, we investigate time series with general distributional assumptions that may show an unknown number of change points in the expectation occurring on multiple time scales and that may also contain change points in other parameters. To that end we propose a multiple filter test (MFT) that tests the null hypothesis of constant expectation and, in case of rejection of the null hypothesis, an algorithm that estimates the change points. The MFT has three important benefits. First, it allows for general distributional assumptions in the underlying model, assuming piecewise sequences of i.i.d. random variables, where also relaxations with regard to identical distribution or independence are possible. Second, it uses a MOSUM type statistic and an asymptotic setting in which the MOSUM process converges weakly to a functional of a Brownian motion which is then used to simulate the rejection threshold of the statistical test. This approach enables a simultaneous application of multiple MOSUM processes which improves the detection of change points that occur on different time scales. Third, we also show that the method is practically robust against changes in other distributional parameters such as the variance or higher order moments which might occur with or even without a change in expectation. A function implementing the described test and change point estimation is available in the R package MFT.

A novel phase I fuzzy profile monitoring approach based on fuzzy change point analysis

In many applications of quality control, the quality of a product or service is described by its profile, which is a relationship between a response variable and one or more independent variables. However, in real world applications, vagueness, imprecision and uncertainty in data is inevitable and hence profile monitoring of fuzzy data is an important issue. In this paper, we discuss the phase I of fuzzy profile monitoring, when the response variables are fuzzy and vague, and propose a new method for estimating the change point. The proposed method, called fuzzy change point technique, is based on the principle of Maximum Likelihood Estimator (MLE) with fuzzy observations. The performance of the proposed method is evaluated by its ability to satisfy the goals of phase I fuzzy profile monitoring and is based on “the probability of an out-of-control signal”, and the accuracy of the change point estimator. Simulation results show that this method outperforms methods known to date. Besides, we are not aware of any other method that is able to determine the real time of change in a process. The applicability of the proposed method is demonstrated by a case study in ceramic tile industry.

Variance Change Point Detection Under a Smoothly-Changing Mean Trend with Application to Liver Procurement

Literature on change point analysis mostly requires a sudden change in the data distribution, either in a few parameters or the distribution as a whole. We are interested in the scenario, where the variance of data may make a significant jump while the mean changes in a smooth fashion. The motivation is a liver procurement experiment monitoring organ surface temperature. Blindly applying the existing methods to the example can yield erroneous change point estimates since the smoothly changing mean violates the sudden-change assumption. We propose a penalized weighted least-squares approach with an iterative estimation procedure that integrates variance change point detection and smooth mean function estimation. The procedure starts with a consistent initial mean estimate ignoring the variance heterogeneity. Given the variance components the mean function is estimated by smoothing splines as the minimizer of the penalized weighted least squares. Given the mean function, we propose a likelihood ratio test statistic for identifying the variance change point. The null distribution of the test statistic is derived together with the rates of convergence of all the parameter estimates. Simulations show excellent performance of the proposed method. Application analysis offers numerical support to non invasive organ viability assessment by surface temperature monitoring. Supplementary materials for this article are available online.

Change-Point Estimation in the Multivariate Model Taking into Account the Dependence: Application to the Vegetative Development of Oilseed Rape

In this paper, we address the change-point estimation issue in multivariate observations which consist in functions having piecewise constant first derivatives corrupted by some additional noise. We propose to solve this problem by rewriting it as a variable selection issue in a sparse multivariate linear model. Moreover, the methodology that we propose takes into account the dependence that may exist within the multivariate observations. Then, the performance of our approach is assessed through some numerical experiments and compared to other alternative and classical methods. Finally, we apply our methodology to experimental data in order to study the vegetative development of oilseed rape. The evolution of the number of leaves of oilseed rape can be modeled as a function having piecewise constant first derivatives corrupted by some additional noise where the change-points correspond to key times in the plant phenology. Our novel estimation method increases the accuracy of the change-point estimation in comparison with classical approaches. Moreover, we show that the parameters of the covariance matrix depend on the level of competition between plants. Supplementary materials accompanying this paper appear online.

Nonparametric change point estimation for survival distributions with a partially constant hazard rate.

We present a new method for estimating a change point in the hazard function of a survival distribution assuming a constant hazard rate after the change point and a decreasing hazard rate before the change point. Our method is based on fitting a stump regression to p values for testing hazard rates in small time intervals. We present three real data examples describing survival patterns of severely ill patients, whose excess mortality rates are known to persist far beyond hospital discharge. For designing survival studies in these patients and for the definition of hospital performance metrics (e.g.mortality), it is essential to define adequate and objective end points. The reliable estimation of a change point will help researchers to identify such end points. By precisely knowing this change point, clinicians can distinguish between the acute phase with high hazard (time elapsed after admission and before the change point was reached), and the chronic phase (time elapsed after the change point) in which hazard is fairly constant. We show in an extensive simulation study that maximum likelihood estimation is not robust in this setting, and we evaluate our new estimation strategy including bootstrap confidence intervals and finite sample bias correction.

Unspecified distributions in single disorder problem

The purpose of this article is to present the issue of algorithms of the change detection model for the political business cycle. Political business cycle issue is interesting in the context of the current political situation in Europe, ie, the progressive integration of the European Union countries and the wave of financial problems that affected the state, which has been regarded so far as economically stable. Monitoring of this phenomenon is characterized by the fact that we do not usually have full information about the behavior of business indexes before and after the change. It is assumed that we are observing a stochastic sequence whose mathematical model predicts a sudden change. The process is Markovian when the change moment is given. The initial problem of disorder detection is transformed to the optimal stopping of the observed sequence. In order to construct an algorithm for estimating the moment of change, we transform the task into an equivalent problem of optimal stopping based on the observed magnitude and some statistics. The analysis obtained from the transformation of the problem is the source of the change point estimation algorithms. The formula for the optimal decision functions is derived.

Change-point estimators with true identification property

The change-point problem is reformulated as a penalized likelihood estimation problem. A new non-convex penalty function is introduced to allow consistent estimation of the number of change points, and their locations and sizes. Penalized likelihood methods based on LASSO and SCAD penalties may not satisfy such a property. The asymptotic properties for the local solutions are established and numerical studies are conducted to highlight their performance. An application to copy number variation is discussed.

A MOSUM procedure for the estimation of multiple random change points

In this work, we investigate statistical properties of change point estimators based on moving sum statistics. We extend results for testing in a classical situation with multiple deterministic change points by allowing for random exogenous change points that arise in Hidden Markov or regime switching models among others. To this end, we consider a multiple mean change model with possible time series errors and prove that the number and location of change points are estimated consistently by this procedure. Additionally, we derive rates of convergence for the estimation of the location of the change points and show that these rates are strict by deriving the limit distribution of properly scaled estimators. Because the small sample behavior depends crucially on how the asymptotic (long-run) variance of the error sequence is estimated, we propose to use moving sum type estimators for the (long-run) variance and derive their asymptotic properties. While they do not estimate the variance consistently at every point in time, they can still be used to consistently estimate the number and location of the changes. In fact, this inconsistency can even lead to more precise estimators for the change points. Finally, some simulations illustrate the behavior of the estimators in small samples showing that its performance is very good compared to existing methods.

Change point detection in network models: Preferential attachment and long range dependence

Inspired by empirical data on real world complex networks, the last few years have seen an explosion in proposed generative models to understand and explain observed properties of real world networks, including power law degree distribution and “small world” distance scaling. In this context, a natural question is how to understand the effect of change points—how abrupt changes in parameters driving the network model change structural properties of the network. We study this phenomenon in one popular class of dynamically evolving networks: preferential attachment models. We derive asymptotic properties of various functionals of the network including the degree distribution as well as maximal degree asymptotics, in essence showing that the change point does effect the degree distribution but does not change the degree exponent. This provides evidence for long range dependence and sensitive dependence of the evolution of the network on the initial evolution of the process. We propose an estimator for the change point and prove consistency properties of this estimator. The methodology developed highlights the effect of the nonergodic nature of the evolution of the network on classical change point estimators.

Estimating the time of a step change in the multivariate-attribute process mean using ANN and MLE

In this paper, we consider correlated multivariate-attribute quality characteristics and provide two methods including a modular method based on artificial neural network (ANN) as well as maximum likelihood estimation (MLE) method to estimate the time of change in the parameters of the process mean. We evaluate the performance of the estimators in terms of some criteria in change point estimation and compare them through simulation studies. The results show that the proposed ANN-based model outperforms the MLE approach under most step shifts in the mean vector of the multivariate-attribute process.

Consistency of the Model Order Change-Point Estimator for GARCH Models

GARCH models have been commonly used to capture volatility dynamics in financial time series. A key assumption utilized is that the series is stationary as this allows for model identifiability. This however violates the volatility clustering property exhibited by financial returns series. Existing methods attribute this phenomenon to parameter change. However, the assumption of fixed model order is too restrictive for long time series. This paper proposes a change-point estimator based on Manhattan distance. The estimator is applicable to GARCH model order change-point detection. Procedures are based on the sample autocorrelation function of squared series. The asymptotic consistency of the estimator is proven theoretically.