# How to measure distance between time series?

Given a quite noisy reference time-series $A$ (about 10k observations), and a bunch of equally sampled time-series $K^i$, is it possible to classify the $K^i$ according to their proximity to $A$? In other words I would like to define a distance measure to the reference time-series.

If it matters my time-series are representing wind speeds, which frequencies are generally well described by a Weibull distribution. But comparing Weibull best-fit parameters is probably not very effective as it discards all information about synchronicity in observations (equal wind speed distributions could come from differently arranged time series).

My first intention was to simply look at the difference $d^i=\sum_t |A_t - K^i_t|$ but it seems a bit of a naive approach. For instance I can imagine that a slight time shift between two otherwise very similar time-series could have very bad such distance. Then there is the Pearson correlation coefficient which looks appropriate but I am not sure if it is really the best approach here.

As I do not have a strong background in data analysis or statistics I would be very grateful if someone could direct me in the right direction about this, and maybe stress out the basic concepts that are involved.

• – Rob Hyndman Jul 11 '17 at 2:26