Bayesian multiscale analysis for time series data

A recently proposed Bayesian multiscale tool for exploratory analysis of time series data is reconsidered and umerous important improvements are suggested. The improvements are in the model itself, the algorithms to analyse it, and how to display the results. The consequence is that exact results can be obtained in real time using only a tiny fraction of the CPU time previously needed to get approximate results. Analysis of both real and synthetic data are given to illustrate our new approach. Multiscale analysis for time series data is a useful tool in applied time series analysis, and with the new model and algorithms, it is also possible to do such analysis in real time.