  Multidimensional time series are sequences of real valued vectors. They occur
in different areas, for example handwritten characters, GPS tracking, and
gestures of modern virtual reality motion controllers. Within these areas, a
common task is to search for similar time series. Dynamic Time Warping (DTW) is
a common distance function to compare two time series. The Edit Distance with
Real Penalty (ERP) and the Dog Keeper Distance (DK) are two more distance
functions on time series. Their behaviour has been analyzed on 1-dimensional
time series. However, it is not easy to evaluate their behaviour in relation to
growing dimensionality. For this reason we propose two new data synthesizers
generating multidimensional time series. The first synthesizer extends the well
known cylinder-bell-funnel (CBF) dataset to multidimensional time series. Here,
each time series has an arbitrary type (cylinder, bell, or funnel) in each
dimension, thus for $d$-dimensional time series there are $3^{d}$ different
classes. The second synthesizer (RAM) creates time series with ideas adapted
from Brownian motions which is a common model of movement in physics. Finally,
we evaluate the applicability of a 1-nearest neighbor classifier using DTW on
datasets generated by our synthesizers.
