  In this paper we are concerned with a sequence of univariate random variables
with piecewise polynomial means and independent sub-Gaussian noise. The
underlying polynomials are allowed to be of arbitrary but fixed degrees. All
the other model parameters are allowed to vary depending on the sample size.
  We propose a two-step estimation procedure based on the $\ell_0$-penalisation
and provide upper bounds on the localisation error. We complement these results
by deriving a global information-theoretic lower bounds, which show that our
two-step estimators are nearly minimax rate-optimal. We also show that our
estimator enjoys near optimally adaptive performance by attaining individual
localisation errors depending on the level of smoothness at individual change
points of the underlying signal. In addition, under a special smoothness
constraint, we provide a minimax lower bound on the localisation errors. This
lower bound is independent of the polynomial orders and is sharper than the
global minimax lower bound.
