Abstract:
We look at the statistical change-point problem in the multivariate setting. In particular, suppose we observe some stochastic process that undergoes a shift to the process mean at an unknown time. We propose a multivariate method for predicting this change-point location by conducting a Bayesian analysis on the empirical detail coefficients of the original time series. We show that if the mean function of our time series is expressed as a multivariate step function, then our Bayesian-wavelet method performs comparably with classical methods such as maximum likelihood estimation (MLE). The advantage to our method is seen in its ability to adapt to more general situations such as piecewise smooth mean functions.