Detecting changes in mean in the presence of time‐varying autocovariance

Abstract

There has been much attention in recent years to the problem of detecting mean changes in a piecewise constant time series. Often, methods assume that the noise can be taken to be independent, identically distributed (IID), which in practice may not be a reasonable assumption. There is comparatively little work studying the problem of mean changepoint detection in time series with nontrivial autocovariance structure. In this article, we propose a likelihood‐based method using wavelets to detect changes in mean in time series that exhibit time‐varying autocovariance. Our proposed technique is shown to work well for time series with a variety of error structures via a simulation study, and we demonstrate its effectiveness on two data examples arising in economics.