Time series distance metric

Question

In order to clusterize a set of time series I\'m looking for a smart distance metric. I\'ve tried some well known metric but no one fits to my case.

ex: Let\'s assume t

Answer 1

nice question! using any standard distance of R^n (euclidean, manhattan or generically minkowski) over those time series cannot achieve the result you want, since those metrics are independent of the permutations of the coordinate of R^n (while time is strictly ordered and it is the phenomenon you want to capture).

A simple trick, that can do what you ask is using the cumulated version of the time series (sum values over time as time increases) and then apply a standard metric. Using the Manhattan metric, you would get as a distance between two time series the area between their cumulated versions.