Two methods for detecting abrupt shifts in the variance, Integrated Cumulative Sum of Squares (ICSS) and Sequential Regime Shift Detector (SRSD), have been compared on both synthetic and observed time series. In Monte Carlo experiments, SRSD outperformed ICSS in the overwhelming majority of the modelled scenarios with different sequences of variance regimes. The SRSD advantage was particularly apparent in the case of outliers in the series. When tested on climatic time series, in most cases both methods detected the same change points in the longer series (252-787 monthly values). The only exception was the Arctic Ocean SST series, when ICSS found one extra change point that appeared to be spurious. As for the shorter time series (66-136 yearly values), ICSS failed to detect any change points even when the variance doubled or tripled from one regime to another. For these time series, SRSD is recommended. Interestingly, all the climatic time series tested, from the Arctic to the Tropics, had one thing in common: the last shift detected in each of these series was toward a high-variance regime. This is consistent with other findings of increased climate variability in recent decades.
Whilst there are a plethora of algorithms for detecting changes in mean in univariate time-series, almost all struggle in real applications where there is autocorrelated noise or where the mean fluctuates locally between the abrupt changes that one wishes to detect. In these cases, default implementations, which are often based on assumptions of a constant mean between changes and independent noise, can lead to substantial over-estimation of the number of changes. We propose a principled approach to detect such abrupt changes that models local fluctuations as a random walk process and autocorr…
A new method of regime shift detection in the correlation coefficient is proposed. The method is designed to find multiple change-points with unknown locations in time series. It signals a possible regime shift in real time and allows for its monitoring. The method is tested on randomly generated time series with predefined change-points. It is applied to examine structural changes in the Bering Sea climate. A major shift is found in 1967, which coincides with a transition from a zonal type of atmospheric circulation to a meridional one. The roles of the Siberian and Alaskan centers of action …
Identifying causal relationships from observational time series data is a key problem in disciplines such as climate science or neuroscience, where experiments are often not possible. Data-driven causal inference is challenging since datasets are often high-dimensional and nonlinear with limited sample sizes. Here we introduce a novel method that flexibly combines linear or nonlinear conditional independence tests with a causal discovery algorithm that allows to reconstruct causal networks from large-scale time series datasets. We validate the method on a well-established climatic teleconnecti…
The Bradley-Terry-Luce (BTL) model is a classic and very popular statistical approach for eliciting a global ranking among a collection of items using pairwise comparison data. In applications in which the comparison outcomes are observed as a time series, it is often the case that data are non-stationary, in the sense that the true underlying ranking changes over time. In this paper we are concerned with localizing the change points in a high-dimensional BTL model with piece-wise constant parameters. We propose novel and practicable algorithms based on dynamic programming that can consistentl…
In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the prop- erties are (approximately) constant for some time and then slowly start to change. In such situations, it is frequently of interest to locate the time point where the properties start to vary. In contrast to the analysis of abrupt changes, methods for detecting smooth or gradual change points are less developed and often require strong paramet- ric assumptions. In this paper, we develop a fully nonparametric method to estimat…
In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the properties are (approximately) constant for some time and then slowly start to change. In many cases, it is of interest to locate the time point where the properties start to vary. In contrast to the analysis of abrupt changes, methods for detecting smooth or gradual change points are less developed and often require strong parametric assumptions. In this paper, we develop a fully nonparametric method to estimate a smooth change po…
We propose a new asymptotic test to assess the stationarity of a time series' mean that is applicable in the presence of both heteroscedasticity and short-range dependence. Our test statistic is composed of Gini's mean difference of local sample means. To analyse its asymptotic behaviour, we develop new limit theory for U-statistics of strongly mixing triangular arrays under non-stationarity. Most importantly, we show asymptotic normality of the test statistic under the hypothesis of a constant mean and prove the test's consistency against a very general class of alternatives, including both s…
Diagnosing the changes of structural behaviors using monitoring data is an important objective of structural health monitoring (SHM). The changes in structural behaviors are usually manifested as the feature changes in monitored structural responses; thus, developing effective methods for automatically detecting such changes is of considerable significance. Existing methods for change detection in SHM are mainly used for scalar or vector data, thus incapable of detecting the changes of the features represented by complex data, e.g., the probability density functions (PDFs). Detecting the abrup…
In modern business modeling and analytics, data monitoring plays a critical role. Nowadays, sophisticated models often rely on hundreds or even thousands of input variables. Over time, structural changes such as abrupt level shifts or trend slope changes may occur among some of these variables, likely due to changes in economy or government policies. As a part of data monitoring, it is important to identify these changepoints, in terms of which variables exhibit such changes, and what time locations do the changepoints occur. Being alerted about the changepoints can help modelers decide if mod…
Real-world systems are often complex, dynamic, and nonlinear. Understanding the dynamics of a system from its observed time series is key to the prediction and control of the system's behavior. While most existing techniques tacitly assume some form of stationarity or continuity, abrupt changes, which are often due to external disturbances or sudden changes in the intrinsic dynamics, are common in time series. Structural breaks, which are time points at which the statistical patterns of a time series change, pose considerable challenges to data analysis. Without identification of such break po…
Variable-intensity astronomical sources are the result of complex and often extreme physical processes. Abrupt changes in source intensity are typically accompanied by equally sudden spectral shifts, i.e., sudden changes in the wavelength distribution of the emission. This article develops a method for modeling photon counts collected from observation of such sources. We embed change points into a marked Poisson process, where photon wavelengths are regarded as marks and both the Poisson intensity parameter and the distribution of the marks are allowed to change. To the best of our knowledge t…
We study detection methods for multivariable signals under dependent noise. The main focus is on three-dimensional signals, i.e. on signals in the space-time domain. Examples for such signals are multifaceted. They include geographic and climatic data as well as image data, that are observed over a fixed time horizon. We assume that the signal is observed as a finite block of noisy samples whereby we are interested in detecting changes from a given reference signal. Our detector statistic is based on a sequential partial sum process, related to classical signal decomposition and reconstruction…
This paper describes a novel approach to change-point detection when the observed high-dimensional data may have missing elements. The performance of classical methods for change-point detection typically scales poorly with the dimensionality of the data, so that a large number of observations are collected after the true change-point before it can be reliably detected. Furthermore, missing components in the observed data handicap conventional approaches. The proposed method addresses these challenges by modeling the dynamic distribution underlying the data as lying close to a time-varying low…
Early warning indicators via latent stochastic dynamical systems
School of Mathematics and Statistics, Huazhong University of Science and Technology（华中科技大学数学与统计学院）；Center for Mathematical Science, Huazhong University of Science and Technology（华中科技大学数学科学中心）；Steklov-Wuhan Institute for Mathematical Exploration, Huazhong University of Science and Technology（华中科技大学斯捷克洛夫-武汉数学探索研究所）；Department of Mathematics and Department of Physics, Great Bay University（大湾区大学数学与物理系）
Detecting abrupt changes in the mean of a time series, so-called changepoints, is important for many applications. However, many procedures rely on the estimation of nuisance parameters (like long-run variance). Under the alternative (a change in mean), estimators might be biased and data-adaptive rules for the choice of tuning parameters might not work as expected. If the data is not stationary, but heteroscedastic, this becomes more challenging. The aim of this paper is to present and investigate two changepoint tests, which involve neither nuisance nor tuning parameters. This is achieved by…
As contemporary software-intensive systems reach increasingly large scale, it is imperative that failure detection schemes be developed to help prevent costly system downtimes. A promising direction towards the construction of such schemes is the exploitation of easily available measurements of system performance characteristics such as average number of processed requests and queue size per unit of time. In this work, we investigate a holistic methodology for detection of abrupt changes in time series data in the presence of quasi-seasonal trends and long-range dependence with a focus on fail…
