  Changepoint models typically assume the data within each segment are
independent and identically distributed conditional on some parameters which
change across segments. This construction may be inadequate when data are
subject to local correlation patterns, often resulting in many more
changepoints fitted than preferable. This article proposes a Bayesian
changepoint model which relaxes the assumption of exchangeability within
segments. The proposed model supposes data within a segment are $m$-dependent
for some unkown $m \geqslant0$ which may vary between segments, resulting in a
model suitable for detecting clear discontinuities in data which are subject to
different local temporal correlations. The approach is suited to both
continuous and discrete data. A novel reversible jump MCMC algorithm is
proposed to sample from the model; in particular, a detailed analysis of the
parameter space is exploited to build proposals for the orders of dependence.
Two applications demonstrate the benefits of the proposed model: computer
network monitoring via change detection in count data, and segmentation of
financial time series.
