  While many approaches have been proposed for discovering abrupt changes in
piecewise constant signals, few methods are available to capture these changes
in piecewise polynomial signals. In this paper, we propose a change point
detection method, PRUTF, based on trend filtering. By providing a comprehensive
dual solution path for trend filtering, PRUTF allows us to discover change
points of the underlying signal for either a given value of the regularization
parameter or a specific number of steps of the algorithm. We demonstrate that
the dual solution path constitutes a Gaussian bridge process that enables us to
derive an exact and efficient stopping rule for terminating the search
algorithm. We also prove that the estimates produced by this algorithm are
asymptotically consistent in pattern recovery. This result holds even in the
case of staircases (consecutive change points of the same sign) in the signal.
Finally, we investigate the performance of our proposed method for various
signals and then compare its performance against some state-of-the-art methods
in the context of change point detection. We apply our method to three
real-world datasets including the UK House Price Index (HPI), the GISS surface
Temperature Analysis (GISTEMP) and the Coronavirus disease (COVID-19) pandemic.
