QA126 : Change Point Detection in the Time Series Data
Thesis > Central Library of Shahrood University > Mathematical Sciences > MSc > 2012
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Abstarct: In a time series can be basically a sequence of observations in order time such as x_1,…,x_n, there many be poimts where in these points, the statistical properties of random variables have been changed. For example, there may be n_0 first observation have distribution F_0 and other observation have distribuation F_1. The point n_0 is called change point and finding this point which the time series features is modified, include a wide range of issues in the real world. Finding the change point is one of the most challenging Statistical issues, because the number and location of these points are unknown. For this purpose several methods have been proposed with different capabilities.
In this thesis, the four methods, cumulative sum (CUSUM) baxsed on bootstrap samples, singular spectrum analysis (SSA), an Bayesian online change point detection (BOCPD) and Bayesian partition production model (PPM) have been studied. In order to verify the accuracy and ability of each of these methods in detecting change points, of three time series simulated and an actual time series are used so that the time series of the simulated are respectively explainer change in surface of the average, change in surface of the variance and change in the autocorrelation. The results of simulated data showed that between the presented methods, Bayesian online change-point detection method, in comparetion whit other methods, has better performance and is able to properly estimated any changes to mentioned. Choosing this method as the best method, real time series data are studied and the performances are compared with other methods. Since the cost time spent for analyze the data and identify of the change is important, the execution time of methods have been compared. The results obtained demonstrate that Bayesian online change-point detection method in large data sets is cost effectiveness.
Keywords:
#time series #the change point #cumulative sum (CUSUM) #Singular spectrum analysis (SSA) #the detection function #matrix heterogeneity #Bayesian online change point detection (BOCPD) #product partition model (PPM)
Keeping place: Central Library of Shahrood University
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Keeping place: Central Library of Shahrood University
Visitor: