A Bayesian wavelet approach to estimation of a change-point in a nonlinear multivariate time series |
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Authors: | Robert M. Steward |
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Affiliation: | Department of Mathematics and Computer Science, Saint Louis University, Saint Louis, MO, USA |
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Abstract: | ABSTRACTWe propose a semiparametric approach to estimate the existence and location of a statistical change-point to a nonlinear multivariate 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 involves conducting a Bayesian analysis on the empirical detail coefficients of the original time series after a wavelet transform. If the mean function of our time series can be expressed as a multivariate step function, we find our Bayesian-wavelet method performs comparably with classical parametric methods such as maximum likelihood estimation. The advantage of our multivariate change-point method is seen in how it applies to a much larger class of mean functions that require only general smoothness conditions. |
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Keywords: | Semiparametric scaling coefficient detail coefficient discrete wavelet transform Haar wavelet |
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