  Dynamic Time Warping (DTW) is a popular time series distance measure that
aligns the points in two series with one another. These alignments support
warping of the time dimension to allow for processes that unfold at differing
rates. The distance is the minimum sum of costs of the resulting alignments
over any allowable warping of the time dimension. The cost of an alignment of
two points is a function of the difference in the values of those points. The
original cost function was the absolute value of this difference. Other cost
functions have been proposed. A popular alternative is the square of the
difference. However, to our knowledge, this is the first investigation of both
the relative impacts of using different cost functions and the potential to
tune cost functions to different tasks. We do so in this paper by using a
tunable cost function {\lambda}{\gamma} with parameter {\gamma}. We show that
higher values of {\gamma} place greater weight on larger pairwise differences,
while lower values place greater weight on smaller pairwise differences. We
demonstrate that training {\gamma} significantly improves the accuracy of both
the DTW nearest neighbor and Proximity Forest classifiers.
