Detect Change Points Research Articles

An empirical analysis of currency volatilities during the recent global financial crisis

This paper investigates the impact of the 2008–2009 global financial crisis on the co-movement of 16 currencies in the sample. It employs a two-step atheoretic empirical methodology; it i) applies change point estimation based on geometric Brownian motion to detect change points in volatilities and ii) applies Engle's (2002) dynamic conditional correlation (DCCR) approach to estimate time varying correlations and then, observes the behavior of volatility co-movements during the periods found in (i). The results show that volatilities increase at least twofold with the outbreak of the crisis and there is an inverse relationship between volatility and the duration of the crisis. The DCCRs usually increase with the onset of the crisis and they fluctuate smoothly afterwards while keeping that increased level.

A New Method of Change Point Detection Using Variable Fuzzy Sets Under Environmental Change

Change point detection is an effective tool to identity whether the hydrological data are of consistency. In this paper, Pettitt test was first used to detect change point for annual rainfall and runoff time series in 6 selected sub-watersheds of Luanhe river basin in Northeast part of China. Then we presented a method to detect change point according to the law of mutual change of quality and quantity in variable fuzzy sets. We chose the mean of time series as assessment index as in other change point detection methods, and defined 95 and 5 % quantiles of the time series as the supremum and infimum respectively. We selected a reference period (for example, the first 10 points of the time series) as the stationary period, and after the reference period, we checked the mean value of the time series point by point. We used this method in the 6 sub-watersheds of Luanhe river basin. The results of the 2 methods showed that most annual rainfall time series had no change point, and some annual runoff time series had change point in 1979 or 1981. Comparison of the 2 methods was made, and it indicated that Pettitt test provided reference for variable fuzzy sets method, but the latter provided more reasonable results than Pettitt test in this study. This method can also be used in other natural time series.

Classifying heartrate by change detection and wavelet methods for emergency physicians

Heart Rate Variability (HRV) carries a wealth of information about the physiological state and the behaviour of a living individual. Indeed, the heart rate variation is intrinsically linked to the autonomic nervous system: the parasympathetic and orthosympathetic systems. Thus, any imbalance in these two opposite systems results in a variation of the cardiac frequency modulation. This alter- nation between equilibrium and disequilibrium (frequency variability) is recognized as an indicator of well-being and good health. Particularly, decreased HRV is linked to stress, fatigue and decreased physical performance. The aim of this work is to exploit the heart rate signals to detect stressful situ- ations in dierent populations: emergency physicians, sportsmen, animal behaviours. . . We introduce a methodological framework for the detection of stress and eventually well-being. Our contribution is rstly based on using Gabor wavelets to extract energies corresponding to High and Low Frequency (HF and LF) bands which are linked to the parasympathetic and orthosympathetic systems. We then detect change points on these energies using the Filtered Derivative with p-value (FDpV) method. Fi- nally, we develop a typology of cardiac activity by distinguishing homogeneous groups or state proles sharing similar characteristics. We apply our methodology on a real dataset collected by monitoring cardiac activity of an emergency physician for 24 hours.

강우자료의 비동질성 규명을 위한 변동점 분석기법의 상호비교 및 적용

Change point analysis is a efficient tool to understand the fundamental information in hydro-meteorological data such as rainfall, discharge, temperature etc. Especially, this fundamental information to change points to future rainfall data identified by reasonable detection skills can affect the prediction of flood and drought occurrence because well detected change points provide a key to resolve the non-stationary or inhomogeneous problem by climate change. Therefore, in this study, the comparative study to assess the performance of the 3 change point detection skills, cumulative sum (CUSUM) method, Bayesian change point (BCP) method, and segmentation by dynamic programming (DP) was performed. After assessment of the performance of the proposed detection skills using the 3 types of the synthetic series, the 2 reasonable detection skills were applied to the observed and future rainfall data at the 5 rainfall gauges in South Korea. Finally, it was suggested that BCP (with 0.9 posterior probability) could be best detection skill and DP could be reasonably recommended through the comparative study. Also it was suggested that BCP (with 0.9 posterior probability) and DP detection skills to find some change points could be reasonable at the North-eastern part in South Korea. In future, the results in this study can be efficiently used to resolve the non-stationary problems in hydrological modeling considering inhomogeneity or nonstationarity.

The CUSUM Test for Detecting Structural Changes in Strong Mixing Processes

Strong mixing property holds for a broad class of linear and nonlinear time series models such as Auto-Regressive Moving Average Processes and Generalized Auto-Regressive Conditional Heteroscedasticity Processes models. In this article, we study correlation structure of strong mixing sequences, and some asymptotic properties are presented. We also present a new method for detecting change point in correlation structure of strong mixing sequences, and present a nonparametric sequential analysis for detecting changes named cumulative sum test statistic for this. Asymptotic consistency of this test statistics is shown. This method is applied to simulated data of some linear and nonlinear models and power of the test is evaluated. For linear models, it is shown that this method has a better performance in comparison to Berkes et al. (2009).

Identification of abrupt changes of the relationship between rainfall and runoff in the Wei River Basin, China

The relationship between rainfall and runoff in the Wei River Basin, one of the most important relationships in hydrology, possibly changed due to the changing climate and increasingly intensifying human activities. The identification of abrupt changes of the relationship will help to further understand the changing mechanism of runoff generation, being a great stimulus to the development of water resources planning and management. Therefore, a new method based on copulas was employed to detect change points of the relationship. Additionally, a Bayesian copula selection method was employed to choose the most appropriate copula, and the primary conclusions are as follows:(1) the Bayesian copula selection method based on Bayesian analysis is independent of parameter selections and easy to implement; (2) the identified change points can be summarized as the early 1970s, the late 1980s, and the middle 1990s; (3) from climate change perspective, the combined impact of increasing air temperature and initially decreasing then increasing potential evaporation had a certain effect on these change points; from human activities perspective, the underlying causes of these change points of the early 1970s, the late 1980s, and the middle 1990s were the construction of water projects and soil conservation, the growing effective arable land of the late 1980s and the growing utilization of water resources in the middle 1990s, respectively. The dominant factor influencing the relation between precipitation and runoff is the increasingly intensifying human activities, and this relation is increasingly weakening.

A Novel Change-Point Detection Approach for Monitoring High-Dimensional Traffics in Distributed Systems

Change-point detection is the problem of finding abrupt changes in time-series. However, the meaningful changes are usually difficult to identify from the original massive traffics, due to high dimension and strong periodicity. In this paper, we propose a novel change-point detection approach, which simultaneously detects change points from all dimensions of the traffics with three steps. We first reduce the dimensions by the classical Principal Component Analysis (PCA), then we apply an extended time-series segmentation method to detect the nontrivial change times, finally we identify the responsible applications for the changes by F-test. We demonstrate through experiments on datasets collected from four distributed systems with 44 applications that the proposed approach can effectively detect the nontrivial change points from the multivariate and periodical traffics. Our approach is more appropriate for mining the nontrivial changes in traffic data comparing with other clustering methods, such as center-based Kmeans and density-based DBSCAN.

Exploring the ability of the Pettitt method for detecting change point by Monte Carlo simulation

The Pettitt method, which is a rank-based test method, has been widely used to detect change point in the mean value of observed series. Traditionally the rank-based test has been assumed to be distribution-free and not sensitive to outliers and skewed distributions. However, there has no evidence provided to prove this assumption. Based on the work of Yue and Wang (Stoch Environ Res Risk Assess 16:307–323, 2002), this study defines the success rate of detecting the given change point as the ability of the Pettitt method, and investigates the ability in various circumstances by means of Monte Carlo simulation. Experiment results demonstrate that, the ability of the Pettitt method depends on not only the pre-assigned significance level, but also various properties of the sample data, including the sample size, the magnitude of a shift and the change point position. Besides, the distribution type and the distribution parameters such as the coefficient of variation, the coefficient of skewness and the shape parameter also seriously influence the ability. As expected, it is easier for the method to detect the change point when the sample size is larger, or the magnitude of a change point is bigger, or the variation of the sample data is smaller. And the highest ability is obtained when the change point occurs at the middle position of the series. These simulation results would provide users an extensive and detailed understanding about the use of the Pettitt method for the detection of change point.

Sequential change detection in the presence of unknown parameters

It is commonly required to detect change points in sequences of random variables. In the most difficult setting of this problem, change detection must be performed sequentially with new observations being constantly received over time. Further, the parameters of both the pre- and post- change distributions may be unknown. In Hawkins and Zamba (Technometrics 47(2):164–173, 2005), the sequential generalised likelihood ratio test was introduced for detecting changes in this context, under the assumption that the observations follow a Gaussian distribution. However, we show that the asymptotic approximation used in their test statistic leads to it being conservative even when a large numbers of observations is available. We propose an improved procedure which is more efficient, in the sense of detecting changes faster, in all situations. We also show that similar issues arise in other parametric change detection contexts, which we illustrate by introducing a novel monitoring procedure for sequences of Exponentially distributed random variable, which is an important topic in time-to-failure modelling.

Seasonality Characteristics and Spatio-temporal Trends of 7-day Low Flows in a Large, Semi-arid Watershed

Seasonality characteristics and spatio-temporal trends of 7-day low flows were investigated for the 41,470 km2 semi-arid Karkheh watershed (western Iran), representing 12 stations with record length of 51 years (1958–2008). Hierarchical Cluster Analysis (HCA) was used to identify low-flow seasonality (clusters of low flow seasons). Monotonic trends were detected by the Mann-Kendall test. Breaks in low flow trends were detected by the Lombard’s change point test. Breaks in short-term trends were detected by the Lepage test. According to results seasonal clusters were different in most of the stations, indicating uniqueness in station low flow behaviour. Among the 12 stations studied, four stations showed seasonal monotonic trend and change points, some with abrupt change (change point in consecutive years). Two stations near watershed outlet with no monotonic trend showed abrupt change. Most seasonal change points (dates) compared well with documented droughts, highlighting drought impacts on low flow trends at affected stations. The Lepage test detected change point in seasonal low flow trends of most stations during 5- and 10-year periods. This research has shown that in semi-arid environments low flow seasonality characteristics may vary among stations, an indication that low flow trends should be evaluated individually for each station.

Gentlemen first? ‘Broken stick’ modelling reveals sex‐related homing decision date in migrating seabirds

AbstractTechnical progress in animal‐borne tracking and movement data analysis has facilitated the understanding of the interplay between successive periods in the life cycle of migratory animals. We investigated how sex differences on the constraints of homing may influence migration to breeding areas in crested penguins (genus Eudyptes). We used a novel approach to infer homing decision date, a precise point in time that translates statistically as a change point in the current distance of the animal to its colony (‘broken stick’ modelling approach, R codes provided here). We applied this approach to geolocation tracking data on migration in three Eudyptes species, from three localities in the southern Indian Ocean (five populations). Sex had a subtle and consistent influence on the temporal activity of the 66 animals during their migratory journey. Males began migration to the breeding localities earlier than females, by an average of 9.1 (range: 4.5–13.5) days. This difference was statistically significant in 4 of 5 populations, and occurred among all species, sites and years surveyed. Our study shows an original application of a recent modelling approach to detect change point in movement data. Our results suggest that sex‐specific constraints related to breeding in migrating animals may also modify activity schedules well before breeding commences.

Homogenization of Chinese daily surface air temperatures and analysis of trends in the extreme temperature indices

This study first homogenizes time series of daily maximum and minimum temperatures recorded at 825 stations in China over the period from 1951 to 2010, using both metadata and the penalized maximum t test with the first‐order autocorrelation being accounted for to detect change points and using the quantile‐matching algorithm to adjust the data time series to diminish discontinuities. Station relocation was found to be the main cause for discontinuities, followed by station automation. The effects of discontinuities on estimation of long‐term trends in the annual mean and extreme indices of temperature are illustrated. The data homogenization is shown to have improved the spatial consistency of estimated trends. Using the homogenized daily minimum and daily maximum temperature data, this study also analyzes trends in extreme temperature indices. The results show that the vast majority (85%–90%) of the 825 sites have experienced significantly more warm nights and less cold nights since 1951. There have also been more warm days and less cold days since 1951, although these trends are less extensive. About 62% of the 825 sites were found to have experienced significantly more warm days and about 50% significantly less cold days. None of the 825 sites were found to have significantly more cold nights/days or less warm nights/days. These indicate that the warming is stronger in nighttime than in daytime and stronger in winter than in summer. Thus, the diurnal temperature range was found to have significantly decreased at 49% of the 825 sites, with significant increases being identified only at 3% of these sites.

Change point detection for neuronal data with CUSUM and classification methods

The visual cortex relies on spikes of retinal ganglion cells (RGC) as the only source of information about the visual environment. In contrast to experimenters, the nervous system generally does not have information about the exact time points of stimulus changes and needs to infer them from RGC population activity. Purpose of change point detection methods is to identify changes in the structure of a time series. Here we want to apply and compare a non-parametric method (classification method) and a parametric method (CUSUM method) for detecting strong changes in population activity referring to stimulus changes. The analyzed data set consists of multi-electrode recordings of RGC. The retina was stimulated with a dot pattern, which moved with one of five different speeds along one axis in two directions (Figure ​(Figure1A).1A). Since acceleration of the pattern increases and deceleration decreases neuronal activity, it is important that change point detection recognizes both types of activity changes. Figure 1 A Velocity of the pattern, (+) movement to the right, (-) to the left. B Change points detected by the classification method. CChange points detected by the CUSUM method. CUSUM is a common change point detection method (e.g. [1]) with several applications in neurobiology (e.g. [2]). The basic step in CUSUM methods consists of recursive calculation of a cumulative sum. Thereby, standardized residues of an assumed parametric model are added. At a change point the value of the cumulative sum exceeds a certain threshold. Hereby, we test for each time point if the Poisson distribution has changed. The idea of the classification method is to use a training data set to learn the statistical properties of the population activity during constant stimulation and in response to stimulus changes. Subsequently, the learned categories are applied to the test data set to calculate for each time point the probability of a stimulus change. A change point is identified when the probability is greater than a threshold, e.g. 0.5. Comparing both methods, the advantage of the CUSUM method is that no training set is required and therefore less pre-analysis is needed. On the other hand, the classification method does not make any assumption of a parametric model. In particular, it does not assume an underlying Poisson process like CUSUM. Both methods show in agreement that stimulus changes can be detected based on the population activity of RGC (Figure ​(Figure1).1). In comparison, the classification method yielded better results. The fraction of correctly detected change points was slightly higher (0.8 compared to 0.7) and the fraction of false positive change points was slightly lower (0.4 compared to 0.5). Moreover, the classification method was found to act on shorter time scales, which might be physiologically more realistic. Considering also the more biologically realistic assumptions of the classification method, these results suggest that this method is superior to the established CUSUM method for the detection of stimulus-triggered changes in neuronal population activity.

Threshold Responses of Forest Birds to Landscape Changes around Exurban Development

Low-density residential development (i.e., exurban development) is often embedded within a matrix of protected areas and natural amenities, raising concern about its ecological consequences. Forest-dependent species are particularly susceptible to human settlement even at low housing densities typical of exurban areas. However, few studies have examined the response of forest birds to this increasingly common form of land conversion. The aim of this study was to assess whether, how, and at what scale forest birds respond to changes in habitat due to exurban growth. We evaluated changes in habitat composition (amount) and configuration (arrangement) for forest and forest-edge species around North America Breeding Bird Survey (BBS) stops between 1986 and 2009. We used Threshold Indicator Taxa Analysis to detect change points in species occurrence at two spatial extents (400-m and 1-km radius buffer). Our results show that exurban development reduced forest cover and increased habitat fragmentation around BBS stops. Forest birds responded nonlinearly to most measures of habitat loss and fragmentation at both the local and landscape extents. However, the strength and even direction of the response changed with the extent for several of the metrics. The majority of forest birds’ responses could be predicted by their habitat preferences indicating that management practices in exurban areas might target the maintenance of forested habitats, for example through easements or more focused management for birds within existing or new protected areas.

A consistent on‐line Bayesian procedure for detecting change points

Bayesian inference on the change points in a given sample is a statistical model selection problem that presents two main difficulties. The first one is the selection of a reasonable prior distribution over the set of models, the number of which depends exponentially on the sample size, and the second is the high computational burden involved even when Markov chain Monte Carlo methods are used.We consider normal linear sampling models for describing the data between consecutive change points, the hierarchical uniform prior over the set of models, intrinsic priors over their model parameters, and to discuss an on‐line Bayesian procedure that alleviates the computational burden for moderate or large sample sizes. Under wide conditions, this procedure is shown to be consistent. Illustrations on simulated and real data sets are given, including the analysis of the change points in the annual mean temperature in central England for the years 1659 to 2011. Copyright © 2013 John Wiley & Sons, Ltd.

Comparison of sequential monitoring methods for environmental time series with stochastic cycle

The paper compares recursive methods for detecting change points in environmental time series. Timely identification of peaks and troughs is important for planning defense actions and preventing risks. We consider linear nonparametric methods, such as time-varying coefficients, double exponential smoothers and prediction error statistics. These methods are often used in surveillance, forecasting and control, and their common features are sequential computation and exponential weighting of data. The new approach proposed here is to select their coefficients by maximizing the difference between subsequent peaks and troughs detected on past data. We compare the methods with applications to meteorological, astronomical and ecological data, and Monte-Carlo simulations.

Data Analysis to Detect Inhomogeneity, Change Points, Trends in Observations: An Application to Po River Discharge Extremes

The aim of this report within GEMINA project is to outline a procedure to detect inhomogeneity, shift, and trends in observed time series. The analysis of hydrological extremes will help to gain insight in the effects at regional/local scale of climate conditions. The same approach will be used to analyze the discharge obtained from numerical simulations that will be carried on in GEMINA project. The main tests for detecting inhomogeneity, change points, and (linear) trend will be presented and the application of tests to detect change points (SNH, Pettitt, Buishand, and Von Neumann) and trend (Mann-Kendall and Spearman) to annual maximum and minimum Po river discharge at the section of Pontelagoscuro is presented. In addition, a Literature review of the applications of the same tests to climate and hydrological variables is provided.

Causality in Scale Space as an Approach to Change Detection

Kernel density estimation and kernel regression are useful ways to visualize and assess the structure of data. Using these techniques we define a temporal scale space as the vector space spanned by bandwidth and a temporal variable. In this space significance regions that reflect a significant derivative in the kernel smooth similar to those of SiZer (Significant Zero-crossings of derivatives) are indicated. Significance regions are established by hypothesis tests for significant gradient at every point in scale space. Causality is imposed onto the space by restricting to kernels with left-bounded or finite support and shifting kernels forward. We show that these adjustments to the methodology enable early detection of changes in time series constituting live surveillance systems of either count data or unevenly sampled measurements. Warning delays are comparable to standard techniques though comparison shows that other techniques may be better suited for single-scale problems. Our method reliably detects change points even with little to no knowledge about the relevant scale of the problem. Hence the technique will be applicable for a large variety of sources without tailoring. Furthermore this technique enables us to obtain a retrospective reliable interval estimate of the time of a change point rather than a point estimate. We apply the technique to disease outbreak detection based on laboratory confirmed cases for pertussis and influenza as well as blood glucose concentration obtained from patients with diabetes type 1.

Application of change point analysis to daily influenza-like illness emergency department visits

BackgroundThe utility of healthcare utilization data from US emergency departments (EDs) for rapid monitoring of changes in influenza-like illness (ILI) activity was highlighted during the recent influenza A (H1N1) pandemic. Monitoring has tended to rely on detection algorithms, such as the Early Aberration Reporting System (EARS), which are limited in their ability to detect subtle changes and identify disease trends.ObjectiveTo evaluate a complementary approach, change point analysis (CPA), for detecting changes in the incidence of ED visits due to ILI.Methodology and principal findingsData collected through the Distribute project (isdsdistribute.org), which aggregates data on ED visits for ILI from over 50 syndromic surveillance systems operated by state or local public health departments were used. The performance was compared of the cumulative sum (CUSUM) CPA method in combination with EARS and the performance of three CPA methods (CUSUM, structural change model and Bayesian) in detecting change points in daily time-series data from four contiguous US states participating in the Distribute network. Simulation data were generated to assess the impact of autocorrelation inherent in these time-series data on CPA performance. The CUSUM CPA method was robust in detecting change points with respect to autocorrelation in time-series data (coverage rates at 90% when −0.2≤ρ≤0.2 and 80% when −0.5≤ρ≤0.5). During the 2008–9 season, 21 change points were detected and ILI trends increased significantly after 12 of these change points and decreased nine times. In the 2009–10 flu season, we detected 11 change points and ILI trends increased significantly after two of these change points and decreased nine times. Using CPA combined with EARS to analyze automatically daily ED-based ILI data, a significant increase was detected of 3% in ILI on April 27, 2009, followed by multiple anomalies in the ensuing days, suggesting the onset of the H1N1 pandemic in the four contiguous states.Conclusions and significanceAs a complementary approach to EARS and other aberration detection methods, the CPA method can be used as a tool to detect subtle changes in time-series data more effectively and determine the moving direction (ie, up, down, or stable) in ILI trends between change points. The combined use of EARS and CPA might greatly improve the accuracy of outbreak detection in syndromic surveillance systems.

Optimal Detection of Changepoints With a Linear Computational Cost

In this article, we consider the problem of detecting multiple changepoints in large datasets. Our focus is on applications where the number of changepoints will increase as we collect more data: for example, in genetics as we analyze larger regions of the genome, or in finance as we observe time series over longer periods. We consider the common approach of detecting changepoints through minimizing a cost function over possible numbers and locations of changepoints. This includes several established procedures for detecting changing points, such as penalized likelihood and minimum description length. We introduce a new method for finding the minimum of such cost functions and hence the optimal number and location of changepoints that has a computational cost, which, under mild conditions, is linear in the number of observations. This compares favorably with existing methods for the same problem whose computational cost can be quadratic or even cubic. In simulation studies, we show that our new method can be orders of magnitude faster than these alternative exact methods. We also compare with the binary segmentation algorithm for identifying changepoints, showing that the exactness of our approach can lead to substantial improvements in the accuracy of the inferred segmentation of the data. This article has supplementary materials available online.