24 August 2015 A Bayesian approach to estimation of a statistical change-point in the mean parameter for high dimensional non-linear time series
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Abstract
We propose a semiparametric approach to infer the existence of and estimate the location of a statistical change-point to a nonlinear high dimensional time series contaminated with an additive noise component. In particular, we consider a p―dimensional stochastic process of independent multivariate normal observations where the mean function varies smoothly except at a single change-point. Our approach first involves a dimension reduction of the original time series through a random matrix multiplication. Next, we conduct a Bayesian analysis on the empirical detail coefficients of this dimensionally reduced time series after a wavelet transform. We also present a means to associate confidence bounds to the conclusions of our results. Aside from being computationally efficient and straight forward to implement, the primary advantage of our methods is seen in how these methods apply to a much larger class of time series whose mean functions are subject to only general smoothness conditions.
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Darrin Speegle, Darrin Speegle, Robert Steward, Robert Steward, } "A Bayesian approach to estimation of a statistical change-point in the mean parameter for high dimensional non-linear time series", Proc. SPIE 9597, Wavelets and Sparsity XVI, 959717 (24 August 2015); doi: 10.1117/12.2187474; https://doi.org/10.1117/12.2187474
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