A Bayesian wavelet approach to estimation of a change-point in a nonlinear multivariate time series

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.

KEYWORDS:

• Semiparametric
• scaling coefficient
• detail coefficient
• discrete wavelet transform
• Haar wavelet

Acknowledgments

We would like to thank both Professor Darrin Speegle and the anonymous referees for their careful consideration of this paper. Their suggestions and helpful advice certainly improved the final form of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.