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Abstract.The broken-stick quantile regression model with multiple change points can characterize a non linear relationship between a response variable and a threshold covariate to change across some values in the domain. However, the estimation and statistical inference of regression coefficients and change points are challenging, due to the non smoothness of the loss function when the locations of the change points are unknown. This article aims to propose a computationally efficient method to estimate the change points and regression coefficients simultaneously via a bent-cable smoothing function that smoothes each change point location in a shrinking neighborhood for prior known the number of change points. The asymptotic properties of the proposed estimators are established. Further, we propose a computationally efficient technique to determine the number of change points for the broken-stick quantile regression model. Monte Carlo simulation results show that the proposed approaches work well in finite samples. Two applications of the maximal running speed data and the global temperature data are used to illustrate the proposed approach. [ABSTRACT FROM AUTHOR]

We consider a regression model with autoregressive terms and propose significance tests for the detection of change points in this model. Our tests are applicable to both low- or moderate dimension and to high-dimension with sparse regressors. The dimension may be high from the practical point of view of economic and business applications, but in our theoretical framework it is fixed. To accommodate practically high dimension, variable selection is incorporated as an integral part of our approach. The regressors and the errors can exhibit general nonlinear dependence and the model incorporates autoregressive dependence. We develop asymptotic justification and evaluate the performance of the tests both on simulated and real economic data. We test for and estimate changes in responses to risk factors of a U.S. energy stocks portfolio and the Industrial Production index. We relate our findings to macroeconomic policy changes and global impact events. [ABSTRACT FROM AUTHOR]

Objective: Cervical cancer (CC), serving as a primary public health challenge, significantly threatens women's health. However, in terms of change-points, there is still a lack of epidemiological studies on the incidence of HPV infection and CC in Xinjiang,China. This research aims to identify significant changes in the trends of HPV infection and CC prevalence in Xinjiang through change-point analysis (CPA) to provide scientific guidance to health authorities. Methods: HPV infection and CC time-series data (from January 2011 to December 2019) were collected and analyzed. Meanwhile, their change-points were detected with binary segmentation method and the PELT method. Furthermore, patients were assigned into three groups based on their different ages and subsequently subjected to an analysis employing a segmented regression model (SRM). Results: It was evident that for the monthly HPV time series, the binary segmentation method detected three change points in August 2015, February 2016, and September 2017 (with the most HPV cases). In contrast, the PELT method detected two change-points in September 2015 and April 2017 (with the most HPV cases). For the monthly CC time series, the binary segmentation method identified two change points in October 2012 and August 2019 (with the most CC cases), whereas the PELT method identified three change points in October 2012, August 2019 (with the most CC cases), and October 2019. The SRM demonstrated varying numbers of change points in distinct groups, with HPV infection and CC having the higher growth rate in the 30–49 and 40–59 age groups, respectively. Based on above results, this research was conductive to comprehending the epidemiology of HPV infection and CC in Xinjiang. In addition, it offered scientific guidance for future prevention and management measures for both HPV infection and CC. [ABSTRACT FROM AUTHOR]

We propose an extension of the preferential attachment scheme by allowing the connecting probability to depend on time t. We estimate the parameters involved in the model by minimizing the expected squared difference between the number of vertices of degree one and its conditional expectation. The asymptotic properties of the estimators are also investigated when the parameters are time-varying by establishing the central limit theorem (CLT) of the number of vertices of degree one. We propose a new statistic to test whether the parameters have change points. We also offer some methods to estimate the number of change points and detect the locations of change points. Simulations are conducted to illustrate the performances of the above results. [ABSTRACT FROM AUTHOR]

Study region: In this study, we compared the spatiotemporal evolution of rainfall trends in E-OBS and ERA5 to those detected using historical rainfall series recorded by ground-based networks in Southern Italy. In particular, the study is applied to the Campania, Basilicata, Apulia, Calabria and Sicily regions (84,000 km2 in total) on seasonal and annual scales. Study focus: Meteorological gridded datasets at large spatial scales are widely used in many hydroclimatic applications as they provide long and spatially homogeneous records. Regional trend analyses based on these data need to be treated with caution due to some potential limitations at relevant hydrological scales, such as the coarse spatial resolution and the spatio-temporal inhomogeneity of the underlying data. Gradual trends and abrupt change points were studied on rainfall data from 1979 to 2019. New hydrological insights for the region: Both gridded datasets capture the major trends in observed rainfall, with a predominance of positive values driven by changes in September-November. Overall, ERA5 returns flatter results compared to E-OBS, with the former comparing well with observations in Sicily and Apulia, while the latter is performing well in Campania and partially in Calabria and Basilicata. Most statistically significant trends are associated with discontinuities in the early 2000s, and this is well captured by both ground and gridded datasets. The general behavior in inter-annual variability trends in Southern Italy is captured by both datasets, with ERA5 also detecting regional patterns.

• Vehicle, cyclist & pedestrian count data from 44 neighboring or collocated stations were analyzed. • Pre & post-pandemic datasets showed pattern changes due to Covid-19 restrictions were mode-specific. • Land-use restrictions and altered trip purposes impacted daily and weekly travel patterns. • Cross-correlation, clustering, and Bayesian change-point analyses showed congruent inferences. • Timeline of pandemic restrictions could be matched using statistical analyses on traffic counts. The spread of Covid-19 and implementation of various restrictions changed how and why people travel. The present study analyzed three different modes of transportation, to understand the impact of Covid-19 mobility and land-use restrictions on chosen neighbourhoods in Dublin City, Ireland. Classification analysis, Spatial correlation analysis, and Bayesian change point analysis had been conducted using vehicle, cyclist & pedestrian count data from 44 neighbouring or collocated stations to explore the statistical changes in the traffic system characteristics. Apart from reduction in traffic counts, the other impacts were modal shift, rise in cyclist numbers, and similarity between weekday & weekend patterns observed. Analyses could identify that changes in the statistical aspects of traffic system are congruent with the changes in lockdown measures. Overall, this study presented a set of tools to identify the existence and degree of changes in traffic patterns over time due to any mobility or land-use policy changes. [ABSTRACT FROM AUTHOR]

Piecewise models play a crucial role in statistical analysis as they allow the same pattern to be adjusted over different regions of the data, achieving a higher quality of fit than would be obtained by fitting them all at once. The standard piecewise linear distribution assumes that the hazard rate is constant between each change point. However, this assumption may be unrealistic in many applications. To address this issue, we introduce a piecewise distribution based on the power-law model. The proposed semi-parametric distribution boasts excellent properties and features a non-constant hazard function between change points. We discuss parameter estimates using the maximum likelihood estimators (MLEs), which yield closed-form expressions for the estimators and the Fisher information matrix for both complete and randomly censored data. Since MLEs can be biased for small samples, we derived bias-corrected MLEs that are unbiased up to the second order and also have closed-form expressions. We consider a profiled MLE approach to estimate change points and construct a hypothesis test to determine the number of change points. We apply our proposed model to analyze the survival pattern of monarchs in the Pharaoh dynasties. Our results indicate that the piecewise power-law distribution fits the data well, suggesting that the lifespans of pharaonic monarchs exhibit varied survival patterns. [ABSTRACT FROM AUTHOR]

The field of whole genomic studies and investigations is currently focused on change-point detection. Over time, various segmentation techniques have been proposed to identify these change points. To effectively locate segments within a genome, it is helpful to pinpoint the intervals or boundaries between them, which are known as change points. By treating these change points as outliers, they can be identified. The anomalies or outliers in a dataset are the observations which are significantly different from the rest of the observations. They can be attributed to some measurement errors or properties of the data themselves. Studying the fluctuations over different segments also revealed the heterogeneity between consecutive segments. In this paper, anomaly identification approach or influential point detection has been discussed and studied in cow genome data of chromosome 25. Furthermore, the observed anomalies have been confirmed to determine whether or not they are true change points. The two-step technique resulted in the identification of change sites based on observed abnormalities and is efficient in terms of calculation time and cost. This study aims to detect any anomalies in genomic data and determine the exact points at which the data segment significantly differed from the rest of the segments. We have developed relevant R codes for data processing and applied methodologies. [ABSTRACT FROM AUTHOR]

Background It is currently unclear whether (and when) physical function exhibits a terminal decline phase, that is, a substantial acceleration of decline in the very last years before death. Methods 702 deceased adults aged 70 years and older from the Yale PEP Study provided 4 133 measurements of physical function (Short Physical Performance Battery, SPPB) up to 20 years before death. In addition, continuous gait and chair rise subtest scores (in seconds) were assessed. Generalized mixed regression models with random change points were used to estimate the onset and the steepness of terminal decline in physical function. Results Decline accelerated in the last years of life in all 3 measures of physical function. The onset of terminal decline occurred 1 year before death for the SPPB, and at 2.5 and 2.6 years before death for chair rise and gait speed test scores, respectively. Terminal declines in physical function were 6–8 times steeper than pre-terminal declines. Relative to those whose condition leading to death was frailty, participants who died from dementia and cancer had an up to 6 months earlier and 3 months later onset of terminal decline in SPPB, respectively. Conclusions Terminal decline in physical function among older adults is comparable to the more established terminal decline phenomenon in cognition. Our results provide additional evidence of late-life rapid decline in physical function due to impending death. [ABSTRACT FROM AUTHOR]

We study a likelihood ratio test for testing the conditional mean of a class of piece-wise stationary CHARN models. We establish the locally asymptotically normal (LAN) structure of the family of likelihoods under study. We prove that the test is asymptotically optimal, and we give an explicit form of its asymptotic local power. We describe an algorithm for detecting change points and estimating their locations. The estimates are obtained as time indices, maximizing the estimate of the local power. The simulation study we conduct shows the good performance of our method on the examples considered. This method is also applied to a set of financial data.

When extrapolating time-to-event data the Bagust and Beale (B&B) approach uses the Kaplan-Meier survival function until a manually chosen time point, after which a constant hazard is assumed. This study demonstrates an objective statistical approach to estimate this time point. We estimate piecewise exponential models (PEMs), whereby the hazard function is partitioned into segments each with constant hazards. The boundaries of these segments are known as change points. Our approach determines the location and number of change points in PEMs from which the hazard in the final segment is used to model long-term survival. We reviewed previous applications of the B&B approach in National Institute for Health and Care Excellence Technology Appraisals (TAs) completed between July 2011 and June 2017. The time points after which constant hazards were assumed were compared between PEMs and the B&B approaches. When further survival data were published following the original TA, we compared these updated estimates to predicted survival from the PEM and other parametric models adjusted for general population mortality. Six of the 59 TAs in this review considered the B&B approach. There was general agreement between the location of time points identified through the PEM and the B&B approaches. In 2 of the identified TAs the best fitting model to the data was a no-change-point model. Of the 3 TAs for which further survival data became available, PEM provided the closest prediction for survival outcomes in 2 TAs. PEMs are useful for survival extrapolation when a long-term constant hazard trend for the disease is clinically plausible. • For clinical and administrative reasons, the early portion of clinical trials can be subject to transient effects that are not representative of the long-term hazards and can potentially bias survival extrapolation. • In this article, we describe a survival model that objectively identifies the location after which disease-related hazards become approximately constant and compare the accuracy of extrapolated survival against other parametric models. • This study illustrates that if disease-related hazards can be assumed constant, the extrapolated survival (adjusting for general population mortality) can be a reasonable estimate for use in decision-analytic model-based cost-effectiveness analysis. [ABSTRACT FROM AUTHOR]

Summary: The fused lasso signal approximator (FLSA) is a smoothing procedure for noisy observations that uses fused lasso penalty on unobserved mean levels to find sparse signal blocks. Several path algorithms have been developed to obtain the whole solution path of the FLSA. However, it is known that the FLSA has model selection inconsistency when the underlying signals have a stair‐case block, where three consecutive signal blocks are either strictly increasing or decreasing. Modified path algorithms for the FLSA have been proposed to guarantee model selection consistency regardless of the stair‐case block. In this paper, we provide a comprehensive review of the path algorithms for the FLSA and prove the properties of the recently modified path algorithms' hitting times. Specifically, we reinterpret the modified path algorithm as the path algorithm for local FLSA problems and reveal the condition that the hitting time for the fusion of the modified path algorithm is not monotone in a tuning parameter. To recover the monotonicity of the solution path, we propose a pathwise adaptive FLSA having monotonicity with similar performance as the modified solution path algorithm. Finally, we apply the proposed method to the number of daily‐confirmed cases of COVID‐19 in Korea to identify the change points of its spread. [ABSTRACT FROM AUTHOR]

In this study, we extend the three‐regime bubble model of Pang et al. (2021, Journal of Econometrics, 221(1):227–311) to allow the forth regime followed by the unit root process after recovery. We provide the asymptotic and finite sample justification of the consistency of the collapse date estimator in the two‐regime AR(1) model. The consistency allows us to split the sample before and after the date of collapse and to consider the estimation of the date of exuberation and date of recovery separately. We have also found that the limiting behavior of the recovery date varies depending on the extent of explosiveness and recovering. [ABSTRACT FROM AUTHOR]

The study of natural and human-made processes often results in long sequences of temporally-ordered values, aka time series (TS). Such processes often consist of multiple states, e.g. operating modes of a machine, such that state changes in the observed processes result in changes in the distribution of shape of the measured values. Time series segmentation (TSS) tries to find such changes in TS post-hoc to deduce changes in the data-generating process. TSS is typically approached as an unsupervised learning problem aiming at the identification of segments distinguishable by some statistical property. Current algorithms for TSS require domain-dependent hyper-parameters to be set by the user, make assumptions about the TS value distribution or the types of detectable changes which limits their applicability. Common hyper-parameters are the measure of segment homogeneity and the number of change points, which are particularly hard to tune for each data set. We present ClaSP, a novel, highly accurate, hyper-parameter-free and domain-agnostic method for TSS. ClaSP hierarchically splits a TS into two parts. A change point is determined by training a binary TS classifier for each possible split point and selecting the one split that is best at identifying subsequences to be from either of the partitions. ClaSP learns its main two model-parameters from the data using two novel bespoke algorithms. In our experimental evaluation using a benchmark of 107 data sets, we show that ClaSP outperforms the state of the art in terms of accuracy and is fast and scalable. Furthermore, we highlight properties of ClaSP using several real-world case studies. [ABSTRACT FROM AUTHOR]

Cross‐batch contamination in a decanter centrifuge during virgin olive oil production cannot be avoided using current technology. The extent of this contamination is investigated using industrial‐scale tests, by measuring the volatile profile and color on three consecutive oil batches, collected at the decanter outlet at different extraction times. The extent of contamination varied, pointing out qualitative consequences, as defective molecules are found. The latter are often active at low concentrations, and the measured cross‐batch contamination can lead both to the downgrading of large batches of virgin olive oils and to the adulteration of monovarietal and certified productions. An innovative method, based on the direct determination of the color (L and a* coordinates) of oil at the outlet of the decanter is able to identify the same compositional change point indicated by gas chromatography, and could be successfully used to mitigate the effects of cross‐batch contamination. Practical applications: An in‐line colorimetric system can be implemented at the decanter outlet to detect the point of change between different olive batches. Otherwise, the virgin olive oil exiting from the decanter at the beginning of one batch can be collected separately in order to avoid the contamination due to the previous batch. [ABSTRACT FROM AUTHOR]

We propose a new methodology for identifying and localizing changes in the Fréchet mean of a multivariate time series of probability densities. The functional data objects we study are random densities f s , t indexed by discrete time t and a vector component s , which can be treated as a broadly understood spatial location. Our main objective is to identify the set of components s , where a change occurs with statistical certainty. A challenge of this analysis is that the densities f s , t are not directly observable and must be estimated from sparse and potentially imbalanced data. Such setups are motivated by the analysis of two data sets that we investigate in this work. First, a hitherto unpublished large data set of Brazilian Covid infections and a second, a financial data set derived from intraday prices of U.S. Exchange Traded Funds. Chief statistical advances are the development of change point tests and estimators of components of change for multivariate time series of densities. We prove the theoretical validity of our methodology and investigate its finite sample performance in a simulation study. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new approach based on the fitting of a generalized linear regression model in order to detect points of change in the variance of a multivariate-covariance Gaussian variable, where the variance function is piecewise constant. By applying this new approach to multivariate waveforms, our method provides simultaneous detection of change points in functional time series. The proposed approach can be used as a new picking algorithm in order to automatically identify the arrival times of P- and S-waves in different seismograms that are recording the same seismic event. A seismogram is a record of ground motion at a measuring station as a function of time, and it typically records motions along three orthogonal axes (X, Y, and Z), with the Z-axis being perpendicular to the Earth's surface and the X- and Y-axes being parallel to the surface and generally oriented in North–South and East–West directions, respectively. The proposed method was tested on a dataset of simulated waveforms in order to capture changes in the performance according to the waveform characteristics. In an application to real seismic data, our results demonstrated the ability of the multivariate algorithm to pick the arrival times in quite noisy waveforms coming from seismic events with low magnitudes. [ABSTRACT FROM AUTHOR]

Affine term structure models are widely used for studying the relationship between yields on assets of different maturities. However, it can be a helpful tool for the construction of fixed-income portfolios. The monitoring of these bond portfolios is of great importance for the investor. The purpose of this work is twofold. Firstly, we construct and optimize fixed-income portfolios using Markowitz's portfolio approach to a multifactor Gaussian affine term structure model (ATSM) under no-arbitrage conditions estimated with the minimum chi square estimation method. The fixed-income portfolios based on the term structure model are compared with some benchmark portfolio strategies, and our findings show that our proposed approach performs well under the risk–return tradeoff. Secondly, we propose control chart procedures for monitoring the optimal weights of government bond portfolios in order to detect possible changes. The results indicate that control chart procedures can be useful in the detection of changes in the optimal asset allocation of fixed income portfolios. [ABSTRACT FROM AUTHOR]

Study region: Asia. Study focus: Hydropower capacity is expected to increase in Asia due to plentiful potential and many investors. Although climate change studies of hydropower have been implemented, most studies have focused on the quantity of change rather than change points. A change point is the time when the plant capacity designed in the past is no longer valid due to climate change, and the efficiency or amount of hydropower can be significantly reduced. Previous studies were constrained to certain stations due to a lack of data. In this study, a method for exploring the change points based on the technical hydropower potential (THP) is proposed with simple data, and the future change points of hydropower in Asia are identified. New hydrological insight for the region: In this study, an approach for detecting the change points of hydropower due to climate change is proposed, and the change points in the Asia are identified. One novelty is the proposed approach is only required discharge and elevation to detect the points. Another novelty is the analysis of THP changes based on different hydropower capacities considering climate change. They have never been discussed and can be utilized for resource expansion and the management of installed plants. Furthermore, the change points are new findings since it has never been reported for most Asia due to limited data availability.

One of the major sources of uncertainty affecting vertical land motion (VLM) estimations are discontinuities and trend changes. Trend changes are most commonly caused by seismic deformation, but can also stem from long-term (decadal to multidecadal) surface loading changes or from local origins. Although these issues have been extensively addressed for Global Navigation Satellite System (GNSS) data, there is limited knowledge of how such events can be directly detected and mitigated in VLM, derived from altimetry and tide-gauge differences (SATTG). In this study, we present a novel Bayesian approach to automatically and simultaneously detect such events, together with the statistics commonly estimated to characterize motion signatures. Next to GNSS time series, for the first time, we directly estimate discontinuities and trend changes in VLM data inferred from SATTG. We show that, compared to estimating a single linear trend, accounting for such variable velocities significantly increases the agreement of SATTG with GNSS values (on average by 0.36 mm/year) at 339 globally distributed station pairs. The Bayesian change point detection is applied to 606 SATTG and 381 GNSS time series. Observed VLM, which is identified as linear (i.e. where no significant trend changes are detected), has a substantially higher consistency with large-scale VLM effects of glacial isostatic adjustment (GIA) and contemporary mass redistribution (CMR). The standard deviation of SATTG (and GNSS) trend differences with respect to GIA+CMR trends is by 38% (and 48%) lower for time series with constant velocity compared to variable velocities. Given that in more than a third of the SATTG time series variable velocities are detected, the results underpin the importance to account for such features, in particular to avoid extrapolation biases of coastal VLM and its influence on relative sea-level-change determination. The Bayesian approach uncovers the potential for a better characterization of SATTG VLM changes on much longer periods and is widely applicable to other geophysical time series. [ABSTRACT FROM AUTHOR]

Reference evapotranspiration (ET0) is a vital component in hydrometeorological research and is widely applied to various aspects, such as water resource management, hydrological modeling, irrigation deployment, and understanding and predicting the influence of hydrologic cycle variations on future climate and land use changes. Quantifying the influence of various meteorological variables on ET0 is not only helpful for predicting actual evapotranspiration but also has important implications for understanding the impact of global climate change on regional water resources. Based on daily data from 69 meteorological stations, the present study analyzed the spatiotemporal pattern of ET0 and major contributing meteorological variables to ET0 from 1960 to 2017 by the segmented regression model, Mann-Kendall test, wavelet analysis, generalized linear model, and detrending method. The results showed that the annual ET0 declined slightly because of the combined effects of the reduction in solar radiation and wind speed and the increase in vapor pressure deficit (VPD) and average air temperature in the Loess Plateau (LP) during the past 58 yr. Four change points were detected in 1972, 1990, 1999, and 2010, and the annual ET0 showed a zigzag change trend of 'increasing-decreasing-increasing-decreasing-increasing'. Wind speed and VPD played a leading role in the ET0 changes from 1960 to 1990 and from 1991 to 2017, respectively. This study confirms that the dominant meteorological factors affecting ET0 had undergone significant changes due to global climate change and vegetation greening in the past 58 years, and VPD had become the major factor controlling the ET0 changes on the LP. The data presented herein will contribute to increasing the accuracy of predictions on future changes in ET0. [ABSTRACT FROM AUTHOR]

Species and interactions are being lost at alarming rates and it is imperative to understand how communities assemble if we have to prevent their collapse and restore lost interactions. Using an 8-year dataset comprising nearly 20 000 pollinator visitation records, we explore the assembly of plant-pollinator communities at native plant restoration sites in an agricultural landscape. We find that species occupy highly dynamic network positions through time, causing the assembly process to be punctuated by major network reorganisations. The most persistent pollinator species are also the most variable in their network positions, contrary to what preferential attachment - the most widely studied theory of ecological network assembly - predicts. Instead, we suggest assembly occurs via an opportunistic attachment process. Our results contribute to our understanding of how communities assembly and how species interactions change through time while helping to inform efforts to reassemble robust communities.

Motivated by the wind turbine anomaly detection, we propose a Bayesian hierarchical model (BHM) for the mean-change detection in multivariate sequences. By combining the exchange random order distribution induced from the Poisson–Dirichlet process and nonlocal priors, BHM exhibits satisfactory performance for mean-shift detection with multivariate sequences under different error distributions. In particular, BHM yields the smallest detection error compared with other competitive methods considered in the article. We use a local scan procedure to accelerate the computation, while the anomaly locations are determined by maximizing the posterior probability through dynamic programming. We establish consistency of the estimated number and locations of the change points and conduct extensive simulations to evaluate the BHM approach. Among the popular change point detection algorithms, BHM yields the best performance for most of the datasets in terms of the F1 score for the wind turbine anomaly detection. [ABSTRACT FROM AUTHOR]

The reliability of a system having some change points is presented. The technique of calculation is based on a previously developed TFCF procedure for evaluating the reliability for i.i.d. component. It involves the use of some auxiliary functions to set up a set of recursive relations. The resultant equations are solved numerically. An extension to the more general TSCSTFCF procedure and its application to start-up demonstration tests is given. Also, in case of testing, the possibility of carrying out simultaneous tests on a set of units is considered.

Objective: Some proposals for oxygen uptake plateau identification are based on linear regression adaptations. However, linear regression does not adequately explain the oxygen uptake nonlinear dynamics. Recently, segmented regression was considered as an alternative to fit this dynamics, by performing an approximation by straight line segments, which provided a satisfactory fit. In this context, the non-plateau and plateau hypotheses were verified by means of a Wald-type test. This work aims to extend these proposals to scenarios with autocorrelated data. Methods: We propose an algorithm to estimate the segmented regression model under autocorrelation using generalized least squares and suggest a bootstrap method to resample from the null distribution of Wald’s statistic. The performance of the estimate and methods of the plateau diagnosis were evaluated via Monte Carlo experiments. Results: The empirical results show that, under autocorrelation, the proposed estimator performs better when compared to the classic method, mainly in scenarios with small sample sizes and moderate/strong autocorrelation structure. The simulations also showed that the plateau diagnosis test has a coherent empirical Type 1 Error probability and good power. Conclusion: We proposed an alternative to estimate the parameters of a segmented regression model for autocorrelated data and an oxygen consumption plateau bootstrap test, and concluded the methods present good performance under simulated and applied case studies. Significance: The proposed method was used to model real oxygen consumption data. Empirical evidence shows that the methods can be used to objectively identify the plateau in oxygen consumption only by specifying a tolerable significance level. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new approach based on the fitting of a generalized linear regression model in order to detect points of change in the variance of a multivariate-covariance Gaussian variable, where the variance function is piecewise constant. By applying this new approach to multivariate waveforms, our method provides simultaneous detection of change points in functional time series. The proposed approach can be used as a new picking algorithm in order to automatically identify the arrival times of P- and S-waves in different seismograms that are recording the same seismic event. A seismogram is a record of ground motion at a measuring station as a function of time, and it typically records motions along three orthogonal axes (X, Y, and Z), with the Z-axis being perpendicular to the Earth’s surface and the X- and Y-axes being parallel to the surface and generally oriented in North–South and East–West directions, respectively. The proposed method was tested on a dataset of simulated waveforms in order to capture changes in the performance according to the waveform characteristics. In an application to real seismic data, our results demonstrated the ability of the multivariate algorithm to pick the arrival times in quite noisy waveforms coming from seismic events with low magnitudes.

Affine term structure models are widely used for studying the relationship between yields on assets of different maturities. However, it can be a helpful tool for the construction of fixed-income portfolios. The monitoring of these bond portfolios is of great importance for the investor. The purpose of this work is twofold. Firstly, we construct and optimize fixed-income portfolios using Markowitz’s portfolio approach to a multifactor Gaussian affine term structure model (ATSM) under no-arbitrage conditions estimated with the minimum chi square estimation method. The fixed-income portfolios based on the term structure model are compared with some benchmark portfolio strategies, and our findings show that our proposed approach performs well under the risk–return tradeoff. Secondly, we propose control chart procedures for monitoring the optimal weights of government bond portfolios in order to detect possible changes. The results indicate that control chart procedures can be useful in the detection of changes in the optimal asset allocation of fixed income portfolios.

Air pollution emissions can exceed the environmental self-purification capacity and trigger hazardous meteorological events, which have non negligible impacts on all aspects of society. The aim of this paper is to study the relationship between China's manufacturing industry benefits and air quality, taking into account the role of government policies in the era of big data, and to study the change points in the time series relationship between industry benefits and air quality. First, we apply and analyze big data and estimate values based on the maximum deviation method. Then, gray relational analysis is used to identify change points, which occur in 2005 and 2010 for both industry benefits and air quality. The total study period is divided into three subperiods: 1998–2005, 2006–2010, and 2011–2017. We find that air pollution control policy was relatively extensive from 1998 to 2005, and that there was a negative relationship between air quality and manufacturing industry benefits. From 2006 to 2010, a positive relationship gradually appeared and, since 2011, with the popularization of big data technology in policy making and environmental governance, intergovernmental cooperation has deepened and manufacturing enterprises have been more actively involved in governance. Consequently, the positive relationship between air quality and the comprehensive benefits of the manufacturing industry has remained stable. Finally, suggestions for policy makers and manufacturing companies are made from the perspectives of system construction, integration, and differentiation, big data challenges, and enterprise innovation. [ABSTRACT FROM AUTHOR]

This article considers the problem of testing temporal homogeneity of p‐dimensional population mean vectors from repeated measurements on n subjects over T times. To cope with the challenges brought about by high‐dimensional longitudinal data, we propose methodology that takes into account not only the "large p, large T, and small n" situation but also the complex temporospatial dependence. We consider both the multivariate analysis of variance problem and the change point problem. The asymptotic distributions of the proposed test statistics are established under mild conditions. In the change point setting, when the null hypothesis of temporal homogeneity is rejected, we further propose a binary segmentation method and show that it is consistent with a rate that explicitly depends on p,T, and n. Simulation studies and an application to fMRI data are provided to demonstrate the performance and applicability of the proposed methods. [ABSTRACT FROM AUTHOR]

Previous studies measure the pricing efficiency of initial public offerings (IPOs) using stochastic frontier analysis, but it is conventionally assumed that all IPOs have the same stochastic frontier function. We study how to measure IPO pricing efficiency under successional issuance policy reforms such as China's Growth Enterprise Market (GEM), where IPOs issued in different time periods might have their own pricing frontiers. In this article, we propose a stochastic frontier model with multiple change points in the time dimension based on the piecewise stochastic frontier function and develop a Bayesian inference and Markov Chain Monte Carlo sampling approach to estimate parameters. An empirical analysis finds two significant structural breaks in the frontier function for China's GEM from October 30, 2009, to January 9, 2018. China's developed provinces have more listed companies but lower average pricing efficiency. After 2012, the average IPO efficiency in public utilities dropped from the first place to the end, but the average IPO efficiency in the conglomerates rosed from the last to the first. Furthermore, a cross‐efficiency analysis proves that gradual market‐oriented issuance mechanism reforms have improved IPO pricing ability. [ABSTRACT FROM AUTHOR]

Temporal and spatial variability of per- and polyfluoroalkyl substances (PFASs) in herring, cod, eelpout, and guillemot covering four decades and more than 1000 km in the Baltic Sea was investigated to evaluate the effect of PFAS regulations and residence times of PFASs. Overall, PFAS concentrations responded rapidly to recent regulations but with some notable basin- and homologue-specific variability. The well-ventilated Kattegat and Bothnian Bay showed a faster log-linear decrease for most PFASs than the Baltic Proper, which lacks a significant loss mechanism. PFOS and FOSA, for example, have decreased with 0-7% y -1 in the Baltic Proper and 6-16% y -1 in other basins. PFNA and partly PFOA are exceptions and continue to show stagnant or increasing concentrations. Further, we found that Bothnian Bay herring contained the highest concentrations of >C 12 perfluoroalkyl carboxylic acids (PFCAs), likely from rivers with high loads of dissolved organic carbon. In the Kattegat, low PFAS concentrations, but a high FOSA fraction, could be due to influence from the North Sea inflow below the halocline and possibly a local source of FOSA and/or isomer-specific biotransformation. This study represents the most comprehensive spatial and temporal investigation of PFASs in Baltic wildlife while providing new insights into cycling of PFASs within the Baltic Sea ecosystem.

AimIn many cases, the dynamics of psychotherapeutic change processes is characterized by sudden and critical transitions. In theoretical terms, these transitions may be “phase transitions” of self-organizing nonlinear systems. Meanwhile, a variety of methods is available to identify phase transitions even in short time series. However, it is still an open question if different methods for timeseries analysis reveal convergent results indicating the moments of critical transitions and related precursors.Methods and ProceduresSeven concepts which are commonly used in nonlinear time series analysis were investigated in terms of their ability to identify changes in psychological time series: Recurrence Plots, Change Point Analysis, Dynamic Complexity, Permutation Entropy, Time Frequency Distributions, Instantaneous Frequency, and Synchronization Pattern Analysis, i.e., the dynamic inter-correlation of the system’s variables. Phase transitions were simulated by shifting control parameters in the Hénon map dynamics, in a simulation model of psychotherapy processes (one by an external shift of the control parameter and one created by a simulated control parameter shift), and three sets of empirical time series generated by daily self-ratings of patients during the treatment.ResultsThe applied methods showed converging results indicating the moments of dynamic transitions within an acceptable tolerance. The convergence of change points was confirmed statistically by a comparison to random surrogates. In the three simulated dynamics with known phase transitions, these could be identified, and in the empirical cases, the methods converged indicating one and the same transition (possibly the phase transitions of the cases). Moreover, changes that did not manifest in a shift of mean or variance could be detected.ConclusionChanges can occur in many different ways in the psychotherapeutic process. For instance, there can be very slow and small transitions or very high and sudden ones. The results show the validity and stability of different measures indicating pattern transitions and/or early warning signals of those transitions. This has profound implications for real-time monitoring in psychotherapy, especially in cases where a transition is not obvious to the eye. Reliably identifying points of change is mandatory also for research on precursors, which in turn can help improving treatment.

In computer science, stochastic processes, and industrial engineering, stationarity is often taken to imply a stable, predictable flow of events and non-stationarity, consequently, a departure from such a flow. Efficient detection and accurate estimation of non-stationarity are crucial in understanding the evolution of the governing dynamics. Pragmatic considerations include protecting human lives and property in the context of devastating processes such as earthquakes or hurricanes. Cumulative Sum (CUSUM) charting, the prevalent technique to weed out such non-stationarities, suffers from assumptions on a priori knowledge of the pre and post-change process parameters and constructs such as time discretization. In this paper, we have proposed two new ways in which non-stationarity may enter an evolving system - an easily detectable way, which we term strong corruption, where the post-change probability distribution is deterministically governed, and an imperceptible way which we term hard detection, where the post-change distribution is a probabilistic mixture of several densities. In addition, by combining the ordinary and switched trend of incoming observations, we develop a new trend ratio statistic in order to detect whether a stationary environment has changed. Surveying a variety of distance metrics, we examine several parametric and non-parametric options in addition to the established CUSUM and find that the trend ratio statistic performs better under the especially difficult scenarios of hard detection. Simulations (both from deterministic and mixed inter-event time densities), sensitivity-specificity type analyses, and estimated time of change distributions enable us to track the ideal detection candidate under various non-stationarities. Applications on two real data sets sampled from volcanology and weather science demonstrate how the estimated change points are in agreement with those obtained in some of our previous works, using different methods. Incidentally, this study sheds light on the inverse nature of dependence between the Hawaiian volcanoes Kilauea and Mauna Loa and demonstrates how inhabitants of the now-restless Kilauea may be relocated to Mauna Loa to minimize the loss of lives and moving costs.

First, using one method of change detection analysis called the cumulative sum, it is possible to detect and characterize regime shifts along the California coast using sea surface temperatures (SSTs) and other variables. Second, physically-determined regime shifts and changes in ocean climatology, determined largely through detailed temperature time-series, can be linked to corresponding changes in biological communities, particularly phytoplankton, which exhibit rapid generation times.

Aim: In many cases, the dynamics of psychotherapeutic change processes is characterized by sudden and critical transitions. In theoretical terms, these transitions may be "phase transitions" of self-organizing nonlinear systems. Meanwhile, a variety of methods is available to identify phase transitions even in short time series. However, it is still an open question if different methods for timeseries analysis reveal convergent results indicating the moments of critical transitions and related precursors. Methods and Procedures: Seven concepts which are commonly used in nonlinear time series analysis were investigated in terms of their ability to identify changes in psychological time series: Recurrence Plots, Change Point Analysis, Dynamic Complexity, Permutation Entropy, Time Frequency Distributions, Instantaneous Frequency, and Synchronization Pattern Analysis, i.e., the dynamic inter-correlation of the system's variables. Phase transitions were simulated by shifting control parameters in the Hénon map dynamics, in a simulation model of psychotherapy processes (one by an external shift of the control parameter and one created by a simulated control parameter shift), and three sets of empirical time series generated by daily self-ratings of patients during the treatment. Results: The applied methods showed converging results indicating the moments of dynamic transitions within an acceptable tolerance. The convergence of change points was confirmed statistically by a comparison to random surrogates. In the three simulated dynamics with known phase transitions, these could be identified, and in the empirical cases, the methods converged indicating one and the same transition (possibly the phase transitions of the cases). Moreover, changes that did not manifest in a shift of mean or variance could be detected. Conclusion: Changes can occur in many different ways in the psychotherapeutic process. For instance, there can be very slow and small transitions or very high and sudden ones. The results show the validity and stability of different measures indicating pattern transitions and/or early warning signals of those transitions. This has profound implications for real-time monitoring in psychotherapy, especially in cases where a transition is not obvious to the eye. Reliably identifying points of change is mandatory also for research on precursors, which in turn can help improving treatment. [ABSTRACT FROM AUTHOR]

A time-domain test for the assumption of second-order stationarity of a functional time series is proposed. The test is based on combining individual cumulative sum tests which are designed to be sensitive to changes in the mean, variance and autocovariance operators, respectively. The combination of their dependent p values relies on a joint-dependent block multiplier bootstrap of the individual test statistics. Conditions under which the proposed combined testing procedure is asymptotically valid under stationarity are provided. A procedure is proposed to automatically choose the block length parameter needed for the construction of the bootstrap. The finite-sample behavior of the proposed test is investigated in Monte Carlo experiments, and an illustration on a real data set is provided. [ABSTRACT FROM AUTHOR]

The K sample problem for high-dimensional vector time series is studied, especially focusing on sensor data streams, in order to analyze the second moment structure and detect changes across samples and/or across variables cumulated sum (CUSUM) statistics of bilinear forms of the sample covariance matrix. In this model, K independent vector time series Y T , 1 , ... , Y T , K are observed over a time span [ 0 , T ] , which may correspond to K sensors (locations) yielding d-dimensional data as well as K locations where d sensors emit univariate data. Unequal sample sizes are considered as arising when the sampling rate of the sensors differs. We provide large-sample approximations and two related change point statistics, a sum of squares and a pooled variance statistic. The resulting procedures are investigated by simulations and illustrated by analyzing a real data set. [ABSTRACT FROM AUTHOR]

This paper considers a robust piecewise linear regression model with an unknown number of change points. Our estimation framework mainly contains two steps: First, we combine the linearization technique with rank-based estimators to estimate the regression coefficients and the location of thresholds simultaneously, given a large number of change points. The associated inferences for all the parameters are easily derived. Second, we use the LARS algorithm via generalized BIC to refine the candidate threshold estimates and obtain the ultimate estimators. The rank-based regression guarantees that our estimators are less sensitive to outliers and heavy-tailed data, and therefore achieves robustness. Simulation studies and an empirical example on BMI and age relationship illustrate the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we propose a method to estimate the number and locations of change points and further estimate parameters of different regions for piecewise stationary vector autoregressive models. The procedure decomposes the problem of change points detection and parameter estimation along the component series. By reformulating the change point detection problem as a variable selection one, we apply group Lasso method to estimate the change points initially. Then, from the preliminary estimate of change points, a subset is selected based on the loss functions of Lasso method and a backward elimination algorithm. Finally, we propose a Lasso + OLS method to estimate the parameters in each segmentation for high-dimensional VAR models. The consistent properties of the estimation for the number and the locations of the change points and the VAR parameters are proved. Simulation experiments and real data examples illustrate the performance of the method. [ABSTRACT FROM AUTHOR]

Let $X_1, X_2,\dots$ be a short-memory linear process of random variables. For $1\leq q , let ${\mathcal{F}}$ be a bounded set of real-valued functions on [0, 1] with finite q-variation. It is proved that $\{n^{-1/2}\sum_{i=1}^nX_i\,f(i/n)\colon f\in{\mathcal{F}}\}$ converges in outer distribution in the Banach space of bounded functions on ${\mathcal{F}}$ as $n\to\infty$. Several applications to a regression model and a multiple change point model are given. [ABSTRACT FROM AUTHOR]