  The problem of time-series clustering is considered in the case where each
data-point is a sample generated by a piecewise stationary ergodic process.
Stationary processes are perhaps the most general class of processes considered
in non-parametric statistics and allow for arbitrary long-range dependence
between variables. Piecewise stationary processes studied here for the first
time in the context of clustering, relax the last remaining assumption in this
model: stationarity. A natural formulation is proposed for this problem and a
notion of consistency is introduced which requires the samples to be placed in
the same cluster if and only if the piecewise stationary distributions that
generate them have the same set of stationary distributions. Simple,
computationally efficient algorithms are proposed and are shown to be
consistent without any additional assumptions beyond piecewise stationarity.
