Inference for multiple change points in time series via likelihood ratio scan statistics

2015 ◽  
Vol 78 (4) ◽  
pp. 895-916 ◽  
Author(s):  
Chun Yip Yau ◽  
Zifeng Zhao
Keyword(s):  
Time Series ◽  
Likelihood Ratio ◽  
Scan Statistics ◽  
Change Points

Testing and estimating change-points in time series

1985 ◽  
Vol 17 (4) ◽  
pp. 841-867 ◽  
Author(s):  
Dominique Picard
Keyword(s):  
Time Series ◽  
Asymptotic Distribution ◽  
Likelihood Ratio ◽  
Asymptotic Properties ◽  
Likelihood Ratio Tests ◽  
Parametric Models ◽  
The Other ◽  
Change Points ◽  
Analysis Of Time Series

The aim of this paper is to present a few techniques which may be useful in the analysis of time series when a failure is suspected. We present two categories of tests and investigate their asymptotic properties: one, of nonparametric type, is intended to detect a general failure in spectrum; the other investigates the properties of likelihood ratio tests in parametric models which have a non-standard behaviour in this situation. Finally, we obtain the asymptotic distribution of the likelihood estimators of the change parameters.

Testing and estimating change-points in time series

1985 ◽  
Vol 17 (04) ◽  
pp. 841-867 ◽  
Author(s):  
Dominique Picard
Keyword(s):  
Time Series ◽  
Asymptotic Distribution ◽  
Likelihood Ratio ◽  
Asymptotic Properties ◽  
Likelihood Ratio Tests ◽  
Parametric Models ◽  
The Other ◽  
Change Points ◽  
Analysis Of Time Series

The aim of this paper is to present a few techniques which may be useful in the analysis of time series when a failure is suspected. We present two categories of tests and investigate their asymptotic properties: one, of nonparametric type, is intended to detect a general failure in spectrum; the other investigates the properties of likelihood ratio tests in parametric models which have a non-standard behaviour in this situation. Finally, we obtain the asymptotic distribution of the likelihood estimators of the change parameters.

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 Changes of China’s agri-food exports to Germany caused by its accession to WTO and the 2008 financial crisis

2015 ◽  
Vol 7 (2) ◽  
pp. 262-279 ◽  
Author(s):  
Zhichao Guo ◽  
Yuanhua Feng ◽  
Thomas Gries
Keyword(s):  
Time Series ◽  
Financial Crisis ◽  
Regression Models ◽  
Structural Breaks ◽  
Global Financial Crisis ◽  
Middle Part ◽  
Change Points ◽  
Content Type ◽  
The World ◽  
Before And After

Purpose – The purpose of this paper is to investigate changes of China’s agri-food exports to Germany caused by China’s accession to WTO and the global financial crisis in a quantitative way. The paper aims to detect structural breaks and compare differences before and after the change points. Design/methodology/approach – The structural breaks detection procedures in this paper can be applied to find out two different types of change points, i.e. in the middle and at the end of one time series. Then time series and regression models are used to compare differences of trade relationship before and after the detected change points. The methods can be employed in any economic series and work well in practice. Findings – The results indicate that structural breaks in 2002 and 2009 are caused by China’s accession to WTO and the financial crisis. Time series and regression models show that the development of China’s exports to Germany in agri-food products has different features in different sub-periods. Before 1999, there is no significant relationship between China’s exports to Germany and Germany’s imports from the world. Between 2002 and 2008 the former depends on the latter very strongly, and China’s exports to Germany developed quickly and stably. It decreased, however suddenly in 2009, caused by the great reduction of Germany’s imports from the world in that year. But China’s market share in Germany still had a small gain. Analysis of two categories in agri-food trade also leads to similar conclusions. Comparing the two events we see rather different patterns even if they both indicate structural breaks in the development of China’s agri-food exports to Germany. Originality/value – This paper partly originally proposes two statistical algorithms for detecting different kinds of structural breaks in the middle part and at the end of a short-time series, respectively.

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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