BOOTSTRAP INFERENCE FOR MULTIPLE CHANGE-POINTS IN TIME SERIES

2021 ◽  
pp. 1-41
Author(s):  
Wai Leong Ng ◽  
Shenyi Pan ◽  
Chun Yip Yau
Keyword(s):  
Time Series ◽  
Change Point ◽  
Financial Time Series ◽  
Change Point Detection ◽  
Stationary Time Series ◽  
Change Points ◽  
Finite Sample ◽  
Sample Distribution ◽  
Stationary Time ◽  
Point Estimators

In this paper, we propose two bootstrap procedures, namely parametric and block bootstrap, to approximate the finite sample distribution of change-point estimators for piecewise stationary time series. The bootstrap procedures are then used to develop a generalized likelihood ratio scan method (GLRSM) for multiple change-point inference in piecewise stationary time series, which estimates the number and locations of change-points and provides a confidence interval for each change-point. The computational complexity of using GLRSM for multiple change-point detection is as low as $O(n(\log n)^{3})$ for a series of length n. Extensive simulation studies are provided to demonstrate the effectiveness of the proposed methodology under different scenarios. Applications to financial time series are also illustrated.

scholarly journals METHOD FOR CHANGE-POINT DETECTION IN PIECEWISE STATIONARY TIME-SERIES

2017 ◽  
Vol 0 (16) ◽  
pp. 120-127
Author(s):  
Олексій Володимирович Дергунов ◽  
Ганна Вадимівна Мартинюк
Keyword(s):  
Time Series ◽  
Change Point ◽  
Change Point Detection ◽  
Stationary Time Series ◽  
Stationary Time ◽  
Point Detection

scholarly journals Nonparametric Anomaly Detection on Time Series of Graphs

2019 ◽  
Author(s):  
Dorcas Ofori-Boateng ◽  
Yulia R. Gel ◽  
Ivor Cribben
Keyword(s):  
Time Series ◽  
Anomaly Detection ◽  
Change Point ◽  
Large Scale ◽  
Dynamic Networks ◽  
Change Point Detection ◽  
New Method ◽  
Global Network ◽  
Change Points ◽  
Finite Sample

AbstractIdentifying change points and/or anomalies in dynamic network structures has become increasingly popular across various domains, from neuroscience to telecommunication to finance. One of the particular objectives of the anomaly detection task from the neuroscience perspective is the reconstruction of the dynamic manner of brain region interactions. However, most statistical methods for detecting anomalies have the following unrealistic limitation for brain studies and beyond: that is, network snapshots at different time points are assumed to be independent. To circumvent this limitation, we propose a distribution-free framework for anomaly detection in dynamic networks. First, we present each network snapshot of the data as a linear object and find its respective univariate characterization via local and global network topological summaries. Second, we adopt a change point detection method for (weakly) dependent time series based on efficient scores, and enhance the finite sample properties of change point method by approximating the asymptotic distribution of the test statistic using the sieve bootstrap. We apply our method to simulated and to real data, particularly, two functional magnetic resonance imaging (fMRI) data sets and the Enron communication graph. We find that our new method delivers impressively accurate and realistic results in terms of identifying locations of true change points compared to the results reported by competing approaches. The new method promises to offer a deeper insight into the large-scale characterizations and functional dynamics of the brain and, more generally, into intrinsic structure of complex dynamic networks.

scholarly journals Bayesian Online Change Point Detection in Finance

2021 ◽  
Vol 17 (4) ◽  
pp. 27-33
Author(s):  
Reza Habibi
Keyword(s):  
Time Series ◽  
Change Point ◽  
Financial Time Series ◽  
Complex Structure ◽  
Change Point Detection ◽  
Change Points ◽  
Bayesian Posterior Probability ◽  
Trading Systems ◽  
Financial Time ◽  
Point Detection

Abstract It is quite common that the structure of a time series changes abruptly. Identifying these change points and describing the model structure in the segments between these change points is an important task in financial time series analysis. Change point detection is the identification of abrupt changes in the generative parameters of sequential data. In application areas such as finance, online rather than offline detection of change points in time series is mostly required, due to their use in predictive tasks, possibly embedded in automatic trading systems. However, the complex structure of the data generation processes makes this a challenging endeavor. This paper is concerned with online change point detection in financial time series using the Bayesian setting. To this end, the Bayesian posterior probability of change at a specific time is proposed and some procedures are presented for selecting the priors and estimation of parameters. Applications in simulated financial time series are given. Finally, conclusions are proposed.

scholarly journals Change Point Enhanced Anomaly Detection for IoT Time Series Data

Water ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 1633
Author(s):  
Elena-Simona Apostol ◽  
Ciprian-Octavian Truică ◽  
Florin Pop ◽  
Christian Esposito
Keyword(s):  
Time Series ◽  
Anomaly Detection ◽  
Change Point ◽  
Time Series Data ◽  
Multivariate Time Series ◽  
Change Point Detection ◽  
Change Points ◽  
Series Data ◽  
Prediction And Forecasting ◽  
Point Detection

Due to the exponential growth of the Internet of Things networks and the massive amount of time series data collected from these networks, it is essential to apply efficient methods for Big Data analysis in order to extract meaningful information and statistics. Anomaly detection is an important part of time series analysis, improving the quality of further analysis, such as prediction and forecasting. Thus, detecting sudden change points with normal behavior and using them to discriminate between abnormal behavior, i.e., outliers, is a crucial step used to minimize the false positive rate and to build accurate machine learning models for prediction and forecasting. In this paper, we propose a rule-based decision system that enhances anomaly detection in multivariate time series using change point detection. Our architecture uses a pipeline that automatically manages to detect real anomalies and remove the false positives introduced by change points. We employ both traditional and deep learning unsupervised algorithms, in total, five anomaly detection and five change point detection algorithms. Additionally, we propose a new confidence metric based on the support for a time series point to be an anomaly and the support for the same point to be a change point. In our experiments, we use a large real-world dataset containing multivariate time series about water consumption collected from smart meters. As an evaluation metric, we use Mean Absolute Error (MAE). The low MAE values show that the algorithms accurately determine anomalies and change points. The experimental results strengthen our assumption that anomaly detection can be improved by determining and removing change points as well as validates the correctness of our proposed rules in real-world scenarios. Furthermore, the proposed rule-based decision support systems enable users to make informed decisions regarding the status of the water distribution network and perform effectively predictive and proactive maintenance.

scholarly journals Closed-Form Estimation of Multiple Change-Point Models

2013 ◽  
Author(s):  
Greg Jensen
Keyword(s):  
Time Series ◽  
Linear Regression ◽  
Change Point ◽  
Marginal Likelihood ◽  
Stationary Time Series ◽  
Change Points ◽  
Model Complexity ◽  
Marginal Model ◽  
General Strategy ◽  
Change Point Models

Identifying discontinuities (or change-points) in otherwise stationary time series is a powerful analytic tool. This paper outlines a general strategy for identifying an unknown number of change-points using elementary principles of Bayesian statistics. Using a strategy of binary partitioning by marginal likelihood, a time series is recursively subdivided on the basis of whether adding divisions (and thus increasing model complexity) yields a justified improvement in the marginal model likelihood. When this approach is combined with the use of conjugate priors, it yields the Conjugate Partitioned Recursion (CPR) algorithm, which identifies change-points without computationally intensive numerical integration. Using the CPR algorithm, methods are described for specifying change-point models drawn from a host of familiar distributions, both discrete (binomial, geometric, Poisson) and continuous (exponential, Gaussian, uniform, and multiple linear regression), as well as multivariate distribution (multinomial, multivariate normal, and multivariate linear regression). Methods by which the CPR algorithm could be extended or modified are discussed, and several detailed applications to data published in psychology and biomedical engineering are described.

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