A Bayesian wavelet approach to estimation of a change-point in a nonlinear multivariate time series. Issue 13 (1st September 2016)

• Record Type: Journal Article
• Authors: Steward, Robert M.; Rigdon, Steven E.
• Is Part Of: Journal of statistical computation and simulation. Volume 86:Issue 13(2016)
• Page Start: 2625
• Page End: 2643
• Publication Date: 2016-09-01
• Subjects: Semiparametric -- scaling coefficient -- detail coefficient -- discrete wavelet transform -- Haar wavelet; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5028505
• DOI: 10.1080/00949655.2015.1116535
• Languages: English
• ISSNs: 0094-9655

Abstract

ABSTRACT: We 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.