  We introduce a new approach for decoupling trends (drift) and changepoints
(shifts) in time series. Our locally adaptive model-based approach for robustly
decoupling combines Bayesian trend filtering and machine learning based
regularization. An over-parameterized Bayesian dynamic linear model (DLM) is
first applied to characterize drift. Then a weighted penalized likelihood
estimator is paired with the estimated DLM posterior distribution to identify
shifts. We show how Bayesian DLMs specified with so-called shrinkage priors can
provide smooth estimates of underlying trends in the presence of complex noise
components. However, their inability to shrink exactly to zero inhibits direct
changepoint detection. In contrast, penalized likelihood methods are highly
effective in locating changepoints. However, they require data with simple
patterns in both signal and noise. The proposed decoupling approach combines
the strengths of both, i.e. the flexibility of Bayesian DLMs with the hard
thresholding property of penalized likelihood estimators, to provide
changepoint analysis in complex, modern settings. The proposed framework is
outlier robust and can identify a variety of changes, including in mean and
slope. It is also easily extended for analysis of parameter shifts in
time-varying parameter models like dynamic regressions. We illustrate the
flexibility and contrast the performance and robustness of our approach with
several alternative methods across a wide range of simulations and application
examples.
