A hierarchical, nonparametric, sequential change-detection test

Electronic Journal of Statistics

This paper is devoted to the offline multiple changes detection for long-range dependent processes. The observations are supposed to satisfy a semi-parametric long-range dependent assumption with distinct memory parameters on each stage. A penalized local Whittle contrast is considered for estimating all the parameters, notably the number of changes. Consistency as well as convergence rates are obtained. Monte-Carlo experiments exhibit the accuracy of the estimators. They also show that the estimation of the number of breaks is improved by using a datadriven slope heuristic procedure of choice of the penalization parameter.

Methodology and Computing in …, 2011

We provide an overview of the state-of-the-art in the area of sequential changepoint detection assuming discrete time and known pre-and post-change distributions. The overview spans over all major formulations of the underlying optimization problem, namely, Bayesian, generalized Bayesian, and minimax. We pay particular attention to the latest advances in each. Also, we link together the generalized Bayesian problem with multi-cyclic disorder detection in a stationary regime when the change occurs at a distant time horizon. We conclude with two case studies to illustrate the cutting edge of the field at work.

Journal of Multivariate Analysis, 2013

The nonparametric test for change-point detection proposed by Gombay and Horváth is revisited and extended in the broader setting of empirical process theory. The resulting testing procedure for potentially multivariate observations is based on a sequential generalization of the functional multiplier central limit theorem and on modifications of Gombay and Horváth's seminal approach that appears to improve the finite-sample behavior of the tests. A large number of candidate test statistics based on processes indexed by lower-left orthants and half-spaces are considered and their performance is studied through extensive Monte Carlo experiments involving univariate, bivariate and trivariate data sets. Finally, practical recommendations are provided and the tests are illustrated on trivariate hydrological data.

The 2011 International Joint Conference on Neural Networks, 2011

This paper presents an online nonparametric methodology based on the Kernel Least Mean Square (KLMS) algorithm and the surprise criterion, which is based on an information theoretic framework. Surprise quantifies the amount of information a datum contains given a known system state, and can be estimated online using Gaussian Process Theory. Based on this concept, we use the KLMS algorithm together with surprise criterion to detect regime change in nonstationary time series. We test the methodology on a synthesized chaotic time series to illustrate this criterion. The results show that surprise criterion is better than the conventional segmentation based on the error criterion.

preprint, 2006

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Arxiv preprint arXiv:0812.1237, 2008

We propose an algorithm for simultaneously detecting and locating changepoints in a time series, and a framework for predicting the distribution of the next point in the series. The kernel of the algorithm is a system of equations that computes, for each index i, the probability that the last (most recent) change point occurred at i. We evaluate this algorithm by applying it to the change point detection problem and comparing it to the generalized likelihood ratio (GLR) algorithm. We find that our algorithm is as good as GLR, or better, over a wide range of scenarios, and that the advantage increases as the signal-to-noise ratio decreases.

Proceedings of the 30th ACM International Conference on Information & Knowledge Management, 2021

2019 IEEE International Conference on Prognostics and Health Management (ICPHM)

Time-series change detection has been studied in several fields. From sensor data, engineering systems, medical diagnosis, and financial markets to user actions on a network, huge amounts of temporal data are generated. There is a need for a clear separation between normal and abnormal behaviour of the system in order to investigate causes or forecast change. Characteristics include irregularities, deviations, anomalies, outliers, novelties or surprising patterns. The efficient detection of such patterns is challenging, especially when constraints need to be taken into account, such as the data velocity, volume, limited time for reacting to events, and the details of the temporal sequence. This paper reviews the main techniques for time series change point detection, focusing on online methods. Performance criteria including complexity, time granularity, and robustness is used to compare techniques, followed by a discussion about current challenges and open issues.

Computational Statistics & Data Analysis

Change point models seek to fit a piecewise regression model with unknown breakpoints to a data set whose parameters are suspected to change through time. However, the exponential number of possible solutions to a multiple change point problem requires an efficient algorithm if long time series are to be analyzed. A sequential Bayesian change point algorithm is introduced that provides uncertainty bounds on both the number and location of change points. The algorithm is able to quickly update itself in linear time as each new data point is recorded and uses the exact posterior distribution to infer whether or not a change point has been observed. Simulation studies illustrate how the algorithm performs under various parameter settings, including detection speeds and error rates, and allow for comparison with several existing multiple change point algorithms. The algorithm is then used to analyze two real data sets, including global surface temperature anomalies over the last 130 years.

Canadian Journal of Statistics, 2020

We consider detection of multiple changes in the distribution of periodic and autocorrelated data with known period. To account for periodicity we transform the sequence of vector observations by arranging them in matrices and thereby producing a sequence of independently and identically distributed matrix observations. We propose methods of testing the equality of matrix distributions and present methods that can be applied to matrix observations using the E‐divisive algorithm. We show that periodicity and autocorrelation degrade existing change detection methods because they blur the changes that these procedures aim to discover. Methods that ignore the periodicity have low power to detect changes in the mean and the variance of periodic time series when the periodic effects overwhelm the true changes, while the proposed methods detect such changes with high power. We illustrate the proposed methods by detecting changes in the water quality of Lake Kasumigaura in Japan. The Canadi...