An Improved Method of Sequential Probability Ratio Test for Change Point Detection in Time Series

2011 ◽  
Author(s):  
Shiro Kihara ◽  
Yoshio Shimizu ◽  
Nobuhiko Morikawa ◽  
Tetsuo Hattori
Keyword(s):  
Time Series ◽  
Change Point ◽  
Sequential Probability Ratio Test ◽  
Change Point Detection ◽  
Ratio Test ◽  
Improved Method ◽  
Probability Ratio ◽  
Sequential Probability ◽  
Point Detection

scholarly journals PERFORMANCE ANALYSIS AND ROBUSTNESS EVALUATION OF A SEQUENTIAL PROBABILITY RATIO TEST FOR NON-IDENTICALLY DISTRIBUTED OBSERVATIONS

2018 ◽  
Vol 54 (2) ◽  
pp. 179-192
Author(s):  
A. Yu. Kharin ◽  
Ton That Tu
Keyword(s):  
Time Series ◽  
Numerical Approach ◽  
Sequential Probability Ratio Test ◽  
Sequential Test ◽  
Ratio Test ◽  
Probability Ratio ◽  
Test Characteristics ◽  
Sequential Probability ◽  
Recursive Calculation ◽  
Likelihood Ratio Statistics

In this article the problem of a sequential test for the model of independent non-identically distributed observations is considered. Based on recursive calculation a new numerical approach to approximate test characteristics for a sequential probability ratio test (SPRT) and a truncated SPRT (TSPRT) is constructed. The problem of robustness evaluation is also studied when the contamination is presented by the distortion of the distributions of all increments of the log-likelihood ratio statistics. The two-side truncated functions are proposed to be used for constructing the robustified SPRT. An algorithm to choose the thresholds of these truncated functions is indicated. The results are applied for a sequential test on parameters of time series with trend. Some kinds of the contaminated models of time series with trend are used to study the robustness of the truncated SPRT. Numerical examples confirming the theoretical results mentioned above are given.

scholarly journals Sequential probability ratio test for many simple hypotheses on parameters of time series with trend

2019 ◽  
pp. 35-45
Author(s):  
Ton That Tu ◽  
Yu. Kharin
Keyword(s):  
Time Series ◽  
Statistical Tests ◽  
Sufficient Conditions ◽  
Sequential Probability Ratio Test ◽  
Sequential Test ◽  
Stopping Times ◽  
Ratio Test ◽  
Probability Ratio ◽  
Sequential Probability ◽  
Finite Moments

The problem of sequential test for many simple hypotheses on parameters of time series with trend is considered. Two approaches, including M-ary sequential probability ratio test and matrix sequential probability ratio test are used for constructing the sequential test. The sufficient conditions of finite terminations of the test and the existence of finite moments of their stopping times are given. The upper bounds for the average numbers of observations are obtained. With the thresholds chosen suitably, these tests can belong to some specified classes of statistical tests. Numerical examples are presented.

scholarly journals Water quality monitoring with online change-point detection methods

2014 ◽  
Vol 17 (1) ◽  
pp. 7-19 ◽  
Author(s):  
Amadou Ba ◽  
Sean A. McKenna
Keyword(s):  
Water Quality ◽  
Time Series ◽  
Change Point ◽  
Change Point Detection ◽  
Ar Model ◽  
Detection Methods ◽  
Ratio Test ◽  
Positive Rate ◽  
Point Detection ◽  
Contamination Events

We develop an approach for water quality time series monitoring and contamination event detection. The approach combines affine projection algorithms and an autoregressive (AR) model to predict water quality time series. Then, we apply online change-point detection methods to the estimated residuals to determine the presence, or not, of contamination events. Particularly, we compare the performance of four change-point detection methods, namely, sequential probability ratio test (SPRT), cumulative sum (CUSUM), binomial event discriminator (BED), and online Bayesian change-point detection (OBCPD), by using residuals obtained from four water quality time series, chlorine, conductivity, total organic carbon, and turbidity. Our fundamental criterion for the performance evaluation of the four change-point detection methods is given by the receiver operating characteristic (ROC) curve which is characterized by the true positive rate as a function of the false positive rate. We highlight with detailed experiments that OBCPD provides the best performance for large contamination events, and we also provide insight on the choice of change-point detection algorithms to consider for designing efficient contamination detection schemes.

scholarly journals Change Point Detection for Diversely Distributed Stochastic Processes Using a Probabilistic Method

Inventions ◽  
2019 ◽  
Vol 4 (3) ◽  
pp. 42
Author(s):  
Muhammad Rizwan Khan ◽  
Biswajit Sarkar
Keyword(s):  
Time Series ◽  
Likelihood Ratio Test ◽  
Data Structures ◽  
Change Point ◽  
Time Series Data ◽  
Probabilistic Method ◽  
Change Point Detection ◽  
Series Data ◽  
Ratio Test ◽  
Point Detection

Unpredicted deviations in time series data are called change points. These unexpected changes indicate transitions between states. Change point detection is a valuable technique in modeling to estimate unanticipated property changes underlying time series data. It can be applied in different areas like climate change detection, human activity analysis, medical condition monitoring and speech and image analyses. Supervised and unsupervised techniques are equally used to identify changes in time series. Even though change point detection algorithms have improved considerably in recent years, several undefended challenges exist. Previous work on change point detection was limited to specific areas; therefore, more studies are required to investigate appropriate change point detection techniques applicable to any data distribution to assess the numerical productivity of any stochastic process. This research is primarily focused on the formulation of an innovative methodology for change point detection of diversely distributed stochastic processes using a probabilistic method with variable data structures. Bayesian inference and a likelihood ratio test are used to detect a change point at an unknown time (k). The likelihood of k is determined and used in the likelihood ratio test. Parameter change must be evaluated by critically analyzing the parameters expectations before and after a change point. Real-time data of particulate matter concentrations at different locations were used for numerical verification, due to diverse features, that is, environment, population densities and transportation vehicle densities. Therefore, this study provides an understanding of how well this recommended model could perform for different data structures.

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