Change-point Estimation Research Articles

Nonparametric multiple change point estimation in highly dependent time series

Given a heterogeneous time-series sample, the objective is to find points in time, called change points, where the probability distribution generating the data has changed. The data are assumed to have been generated by arbitrary unknown stationary ergodic distributions. No modelling, independence or mixing assumptions are made. A novel, computationally efficient, nonparametric method is proposed, and is shown to be asymptotically consistent in this general framework. The theoretical results are complemented with experimental evaluations.

Estimation and identification of change points in panel models with nonstationary or stationary regressors and error term

ABSTRACTThis article studies the estimation of change point in panel models. We extend Bai (2010) and Feng et al. (2009) to the case of stationary or nonstationary regressors and error term, and whether the change point is present or not. We prove consistency and derive the asymptotic distributions of the Ordinary Least Squares (OLS) and First Difference (FD) estimators. We find that the FD estimator is robust for all cases considered.

Estimation of heterogeneous panels with structural breaks

This paper extends Pesaran’s (2006) work on common correlated effects (CCE) estimators for large heterogeneous panels with a general multifactor error structure by allowing for unknown common structural breaks. Structural breaks due to new policy implementation or major technological shocks, are more likely to occur over a longer time span. Consequently, ignoring structural breaks may lead to inconsistent estimation and invalid inference. We propose a general framework that includes heterogeneous panel data models and structural break models as special cases. The least squares method proposed by Bai (1997a, 2010) is applied to estimate the common change points, and the consistency of the estimated change points is established. We find that the CCE estimator have the same asymptotic distribution as if the true change points were known. Additionally, Monte Carlo simulations are used to verify the main results of this paper.

Change Point Analysis of Exchange Rates Using Bootstrapping Methods: An Application to the Indonesian Rupiah 2000–2008

In this paper, we investigate detecting single change point under time series regression model with GARCH errors using the cumulative sum of squares of the least squares residuals test and the log-likelihood ratio test. Furthermore we think it is important to calculate confidence interval for an estimated change point, for which we need to know the sampling distribution of the estimated change point. We obtain the sampling distribution to calculate confidence interval using Monte Carlo simulation based on a circular block bootstrap method and verify the performance of the above break point tests by Monte Carlo experiment. Then we detect a change point in the exchange rate of Indonesian Rupiah (IDR) using the above test to detect. The Government of Indonesia officially announced (de jure) to adopt a floating exchange rate regime in August 1997. However, from time to time, Bank Indonesia nevertheless maintains the stability of rupiah value in the market. Since there is no official information regarding on central bank’s intervention in the foreign exchange market, therefore detecting a structural change in the time series of the exchange market can be used as an indicator of exchange rate management. Our real data analysis shows that the IDR had been moving with the USD since 2000, but that the direction of the relationship changed in March 2002. This indicates that there was some control over the Rupiah’s movement.

Erratum to: Testing structural changes in panel data with small fixed panel size and bootstrap

In the original publication, the form of the change point estimate presented in Section 4 is not suitable. The correct form of the estimate with correct assertion of Theorem 3 is given below. The corrected version of the original paper can be found on arXiv http://arxiv.org/abs/1509.01291. Having a sequence of weights {w(t)}T t=2, let us define the estimate of τ as τN := arg min t=2,...,T 1 w(t) N ∑

Effect of increasing amounts of straw on pigs’ explorative behaviour

According to European legislation, pigs must have permanent access to sufficient quantity of material to enable manipulation activities. However, few studies have quantified how much straw is needed to fulfil the requirements of growing pigs. We investigated the effect of increasing amount of straw on pigs’ manipulation of the straw, and hypothesised that after a certain point increasing straw amount will no longer increase oral manipulation further. From 30 to 80kg live weight, pigs were housed in 90 groups of 18 pigs in pens (5.48m×2.48m) with partly slatted concrete floor and daily provided with fresh uncut straw onto the solid part of the floor. Experimental treatments were 10, 80, 150, 220, 290, 360, 430 or 500g straw per pig and day. At 40 and 80kg live weight, the time spent in oral manipulation of the straw by three focal pigs per pen (large, medium and small sized) were recorded along with the percentage of pigs manipulating straw simultaneously. This was recorded in three 1-h intervals (1h before and 1h after straw allocation in the morning, as well as from 17 to 18h in the afternoon). With increasing quantity of straw provided, we found a curvilinear (P<0.01) increase in the time spent in oral manipulation of the straw. Smaller pigs spent more time manipulating straw than larger and medium sized pigs (367, 274 and 252s/h for small, medium and large sized pigs, respectively; P<0.001), and pigs spent more time manipulating straw at 40kg than 80kg live weight (356 vs. 250s/h; P<0.001). At both live weights, pigs spent most time manipulating straw during the hour after allocation of straw. Similar effects of increasing amounts of straw were found for the percentage of pigs engaged in simultaneous manipulation of the straw. Post hoc analyses were applied to estimate the point, after which additional straw did not increase manipulation of straw any further. For the time spent manipulating straw the estimated change point was 253 (approx. 95% confidence limits (CL) 148–358) g straw per pig and day. For the number of pigs simultaneously manipulating straw the change point was 248 (CL 191–304) g straw per pig and day. These results show that increasing the quantity of straw from minimal to approximately 250g per pig and day increased the time spent in oral manipulation of the straw, as well as the occurrence of simultaneous straw manipulation.Hence, data from the current experiment identified 250g straw per pig per day as the amount of straw where a further increase in straw provision did not further increase neither time spent on oral manipulation of straw, nor the percentage of pigs simultaneously manipulating straw. This suggests that, within the current housing system and using this criterion, this amount of straw may be the biological turning point for increasing oral manipulation of straw.

Composite change point estimation for bent line quantile regression

The bent line quantile regression describes the situation where the conditional quantile function of the response is piecewise linear but still continuous in covariates. In some applications, the change points at which the quantile functions are bent tend to be the same across quantile levels or for quantile levels lying in a certain region. To capture such commonality, we propose a composite estimation procedure to estimate model parameters and the common change point by combining information across quantiles. We establish the asymptotic properties of the proposed estimator, and demonstrate the efficiency gain of the composite change point estimator over that obtained at a single quantile level through numerical studies. In addition, three different inference procedures are proposed and compared for hypothesis testing and the construction of confidence intervals. The finite sample performance of the proposed procedures is assessed through a simulation study and the analysis of a real data.

Changepoint estimation: another look at multiple testing problems

SUMMARY We consider large scale multiple testing for data that have locally clustered signals. With this structure, we apply techniques from change-point analysis and propose a boundary detection algorithm so that the clustering information can be utilised. Consequently the precision of the multiple testing procedure is substantially improved. We study tests with independent as well as dependent p-values. Monte Carlo simulations suggest that the methods perform well with realistic sample sizes and show improved detection ability compared with competing methods. Our procedure is applied to a genome-wide association dataset of blood lipids.

Step change point estimation in the multivariate-attribute process variability using artificial neural networks and maximum likelihood estimation

In some statistical process control applications, the combination of both variable and attribute quality characteristics which are correlated represents the quality of the product or the process. In such processes, identification the time of manifesting the out-of-control states can help the quality engineers to eliminate the assignable causes through proper corrective actions. In this paper, first we use an artificial neural network (ANN)-based method in the literature for detecting the variance shifts as well as diagnosing the sources of variation in the multivariate-attribute processes. Then, based on the quality characteristics responsible for the out-of-control state, we propose a modular model based on the ANN for estimating the time of step change in the multivariate-attribute process variability. We also compare the performance of the ANN-based estimator with the estimator based on maximum likelihood method (MLE). A numerical example based on simulation study is used to evaluate the performance of the estimators in terms of the accuracy and precision criteria. The results of the simulation study show that the proposed ANN-based estimator outperforms the MLE estimator under different out-of-control scenarios where different shift magnitudes in the covariance matrix of multivariate-attribute quality characteristics are manifested.

Inference for post-change parameters after sequential CUSUM test under AR(1) model

For a sequence of correlated normal random variables following the AR(1) change-point model, the inference problem for the change-point and post-change mean is considered when the residuals are used to form the sequential model-based CUSUM procedure. Higher order biases and corrected pivots are developed to construct confidence intervals. Numerical comparison with the classical CUSUM procedure shows that the model-based CUSUM procedure has smaller average delay detection time and change-point estimation bias. Northern hemisphere average temperature data is used for illustration.

Isotonic Change Point Estimation in the AR(1) Autocorrelated Simple Linear Profiles

Sometimes the relationship between dependent and explanatory variable(s) known as profile is monitored. Simple linear profiles among the other types of profiles have been more considered due to their applications especially in calibration. There are some studies on the monitoring them when the observations within each profile are autocorrelated. On the other hand, estimating the change point leads to meet great saving time and costs. Hence, in this paper, a maximum likelihood estimator is derived for simple linear profiles with first order autoregressive autocorrelation structure within each profile to estimate monotonic change point. The performance of the proposed estimator is appraised and compared to estimators that derived under step change and drift and a confidence set estimator presented. The results demonstrate that the proposed estimator has better performance in small and medium shifts whereas the performance of their corresponding estimators becomes better than the proposed estimator in large shifts. It is worth mentioning that knowing type of the change is not important in the proposed estimator and its only assumption is belonging of the change type to a family of monotonic shifts. Finally, the performance of the estimator is illustrated through a real case.

Drift Change Point Estimation in Autocorrelated Poisson Count Processes Using MLE Approach

Drift Change Point Estimation in Autocorrelated Poisson Count Processes Using MLE Approach

Panel data segmentation under finite time horizon

We study the nonparametric change point estimation for common changes in the means of panel data. The consistency of estimates is investigated when the number of panels tends to infinity but the sample size remains finite. Our focus is on weighted denoising estimates, involving the group fused LASSO, and on the weighted CUSUM estimates. Due to the fixed sample size, the common weighting schemes do not guarantee consistency under (serial) dependence and most typical weightings do not even provide consistency in the i.i.d. setting when the noise is too dominant.Hence, on the one hand, we propose a consistent covariance-based extension of existing weighting schemes and discuss straightforward estimates of those weighting schemes. The performance will be demonstrated empirically in a simulation study. On the other hand, we derive sharp bounds on the change to noise ratio that ensure consistency in the i.i.d. setting for classical weightings.

Identifying the time of a step change in AR(1) auto-correlated simple linear profiles

Assuming a first-order auto-regressive model for the auto-correlation structure between observations, in this paper, a transformation method is first employed to eliminate the effect of auto-correlation. Then, a maximum likelihood estimator (MLE) of a step change in the parameters of the transformed model is derived and three separate EWMA control charts are used to monitor the parameters of the profile. The performance of the proposed change-point estimator is next compared to the one of the built-in change-point estimator of EWMA control chart through some simulation experiments. The results show that the proposed MLE of the change point accurately estimates the true change point and outperforms the built-in estimator of EWMA chart for almost all shift values and auto-correlation coefficients, while the built-in estimator of EWMA chart, in general, underestimates the true change point.

Monitoring and change-point estimation for spline-modeled non-linear profiles in phase II

In some applications of statistical quality control, quality of a process or a product is best characterized by a functional relationship between a response variable and one or more explanatory variables. This relationship is referred to as a profile. In certain cases, the quality of a process or a product is better described by a non-linear profile which does not follow a specific parametric model. In these circumstances, nonparametric approaches with greater flexibility in modeling the complicated profiles are adopted. In this research, the spline smoothing method is used to model a complicated non-linear profile and the Hotelling T2 control chart based on the spline coefficients is used to monitor the process. After receiving an out-of-control signal, a maximum likelihood estimator is employed for change point estimation. The simulation studies, which include both global and local shifts, provide appropriate evaluation of the performance of the proposed estimation and monitoring procedure. The results indicate that the proposed method detects large global shifts while it is very sensitive in detecting local shifts.

The end of the decline in cervical cancer mortality in Spain: trends across the period 1981-2012.

BackgroundIn Spain, cervical cancer prevention is based on opportunistic screening, due to the disease’s traditionally low incidence and mortality rates. Changes in sexual behaviour, tourism and migration have, however, modified the probability of exposure to human papilloma virus among Spaniards. This study thus sought to evaluate recent cervical cancer mortality trends in Spain.MethodsWe used annual female population figures and individual records of deaths certified as cancer of cervix, reclassifying deaths recorded as unspecified uterine cancer to correct coding quality problems. Joinpoint models were fitted to estimate change points in trends, as well as the annual (APC) and average annual percentage change. Log-linear Poisson models were also used to study age-period-cohort effects on mortality trends and their change points.Results1981 marked the beginning of a decline in cervical cancer mortality (APC1981–2003: −3.2; 95% CI:-3.4;-3.0) that ended in 2003, with rates reaching a plateau in the last decade (APC2003–2012: 0.1; 95% CI:-0.9; 1.2). This trend, which was observable among women aged 45–46 years (APC2003–2012: 1.4; 95% CI:-0.1;2.9) and over 65 years (APC2003–2012: −0.1; 95% CI:-1.9;1.7), was clearest in Spain’s Mediterranean and Southern regions.ConclusionsThe positive influence of opportunistic screening is not strong enough to further reduce cervical cancer mortality rates in the country. Our results suggest that the Spanish Health Authorities should reform current prevention programmes and surveillance strategies in order to confront the challenges posed by cervical cancer.Electronic supplementary materialThe online version of this article (doi:10.1186/s12885-015-1306-x) contains supplementary material, which is available to authorized users.

A change-point problem in relative error-based regression

A nonparametric relative error-based method is proposed to detect and estimate the change point for the multiplicative regression models. The asymptotic distribution of the proposed test statistic for no change-point effect is established. We prove the \(n\)-consistency of the proposed estimator of the change point. Simulation studies demonstrate that change-point detection and estimation with relative errors perform reasonably well in many practical situations. Application is illustrated with a financial dataset.

Change Point Estimation in the Mean of Multivariate Linear Profiles with No Change Type Assumption via Dynamic Linear Model

Change point estimation is a useful concept that helps quality engineers to effectively search for assignable causes and improve quality of the process or product. In this paper, the maximum likelihood approach is developed to estimate change point in the mean of multivariate linear profiles in Phase II. After the change point, parameters are estimated through filtering and smoothing approaches in dynamic linear model. The proposed change point estimator can be applied without any prior knowledge about the change type against existing estimators which assume change type is known in advance. Besides, sporadic change point can be identified as well. Simulation results show the effectiveness of the proposed estimators to estimate step, drift and monotonic, as well as sporadic changes in small to large shifts. In addition, effect of different values of the Multivariate Exponentially Weighted Moving Average (MEWMA) control chart smoothing coefficient on the performance of the proposed estimator is investigated presenting that the smoothing estimator has more uniform performance. Copyright © 2015 John Wiley & Sons, Ltd.

The LAD estimation of the change-point linear model with randomly censored data

In this paper, a change-point linear model with randomly censored data is investigated. We propose the least absolute deviation estimation procedure for regression and change-point parameters simultaneously. The asymptotic properties of the change-point and regression parameter estimators are obtained. We show that the resulting regression parameter estimator is asymptotically normal, and the change-point estimator converges weakly to the minimizer of a given random process. The extensive simulation studies and the analysis of an acute myocardial infarction data set are conducted to illustrate the finite sample performance of the proposed method.

Graph-based change-point detection

We consider the testing and estimation of change-points—locations where the distribution abruptly changes—in a data sequence. A new approach, based on scan statistics utilizing graphs representing the similarity between observations, is proposed. The graph-based approach is nonparametric, and can be applied to any data set as long as an informative similarity measure on the sample space can be defined. Accurate analytic approximations to the significance of graph-based scan statistics for both the single change-point and the changed interval alternatives are provided. Simulations reveal that the new approach has better power than existing approaches when the dimension of the data is moderate to high. The new approach is illustrated on two applications: The determination of authorship of a classic novel, and the detection of change in a network over time.