  In a wide range of modern applications, we observe a large number of time
series rather than only a single one. It is often natural to suppose that there
is some group structure in the observed time series. When each time series is
modelled by a nonparametric regression equation, one may in particular assume
that the observed time series can be partitioned into a small number of groups
whose members share the same nonparametric regression function. We develop a
bandwidth-free clustering method to estimate the unknown group structure from
the data. More precisely speaking, we construct multiscale estimators of the
unknown groups and their unknown number which are free of classical bandwidth
or smoothing parameters. In the theoretical part of the paper, we analyze the
statistical properties of our estimators. Our theoretical results are derived
under general conditions which allow the data to be dependent both in time
series direction and across different time series. The technical analysis of
the paper is complemented by a simulation study and a real-data application.
