Structural Change Point Detection Method of Time Series Using Sequential Probability Ratio Test

Abstract

This paper concerns early change detection problem in time series. For the early detection problem, we propose an application of Sequential Probability Ratio Test (SPRT) that has been mainly used in the field of quality control. The SPRT is used for testing a null hypothesis H 0 (e.g. the quality is under pre-specified limit 1%) against hypothesis H 1 (e.g. the quality is over pre-specified limit 1%). And it is defined as follows: At each stage of successive observations on data Z 1 ,Z 2 , …, the probability ratio λ i is computed.

Model Introduced SPRT for Structural Change Detection of Time Series (II)

“…The SPRT and NSPR can detect the change point correctly from the sequence of image data. We show experimental results of change detection using two tests (SPRT and Chow Test 6,7,8 ) and one ratio of NSPR.…”

“…For the second change detection problem, we previously proposed an application of SPRT (Sequential Probability Ratio Test) that has been mainly used in the field of quality control. [5][6][7][8] In this paper, using the notion of a binary Channel as well known in Information Theory, we present an equivalent relation between the SPRT and Bayes' Updating. Moreover, we also explain the relation between the SPRT and the New Sequential Probability Ratio of two conditional probabilities when a Hidden Markov Model with Poisson process is introduced as the never returning structural change model.…”

“…Example of regression line as a predicted model. 6 In this experimentation, the prediction model is single regression line and the model is constructed by the first six images, i.e., No.1 through No.6 image. And the tolerable zone is the range of 2σ from the predicted value as shown in Fig.7.…”

“…And the tolerable zone is the range of 2σ from the predicted value as shown in Fig.7. 6 The results of change detection by the two Tests (SPRT and Chow Test) and NSPR are shown in the graph of Fig.8.…”

An Information Theoretic Methodology for Kansei Engineering: Kansei Channel and Subjective Probability

“…And, using the notion of Binary Channel, we present a relation between the Bayes' Updating [5] and Sequential Probability Ratio Test (SPRT) [10]- [12]. Moreover, we show a possibility that the computation of Optimal Input Probability Distribution (OIPD) of Channel Capacity ([6]- [9]) can be a powerful tool of Clustering Analysis.…”