Time series regression with persistent level shifts

A changepoint in a time series is a time in which any change in the distributional form (marginal or joint) of the series occurs. This includes changes in mean or covariance structure of the time series. Mean level shift changepoints have been shown to dramatically influence linear trend estimates obtained from a simple linear regression model. This study provides an asymptotic analysis of a time series regression model experiencing an increasing number of mean level shifts at known times. It is shown that one may consistently estimate any finite number of unknown parameters in a time series polynomial regression, so long as two or more consecutive observations without a changepoint occurs infinity often in the limit.