Advances and Applications in Statistics
Volume 53, Issue 4, Pages 363 - 378
(October 2018) http://dx.doi.org/10.17654/AS053040363 |
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COMPARISON OF DIFFERENT WAVELET TECHNIQUES FOR FINDING CHANGE POINTS
Arunendu Chatterjee
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Abstract: We use wavelets within a Bayesian framework to identify changes in the form of shifts in data collected over time in the presence of noise and missing observations. We modify and extend an existing Bayesian change point detection procedure due to Ogden and Lynch [11] which uses the discrete wavelet transform. Our main objective is to investigate the usefulness of the procedure for real data sets, and to modify it by using one of the more recent lifting transform to identify change points, specifically using an adaptive lifting procedure due to Nunes et al. [10]. Our research was motivated by a problem encountered in the analysis of water pressure data. To that effect, we first conducted a simulation study based on which, we provide recommendations for the choice of lifting-based wavelet coefficients to be used in the change point detection procedure in the context of different jump sizes, noise variances and missing observations. We present results for other real data problems from the change point literature where the existence and timing of change points are known. |
Keywords and phrases: Bayesian method, lifting.
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