How to measure similarity in "Direction of Change" in two time series

Question

I am looking for a method to compare two time series. I know various of method exists and since I have very specific needs I decided to post this thread. First of all, here I define similarity as "direction of change" of two time series more than classic Euclidean distance between each pair of points. Example when two series I believe are similar is:

Regular Pearson Coefficient is equals to 0,74. I believe it does not represent strength in direction of change similarity. When you look closely to this example chart only differences exist between time periods 4 and 5, where red went up and blue went down also between 13 and 14 when blue went little bit up and red down. My time series are specific:

• they are stationary, so I dont think any cointegration test are appropriate here

• all compared time series are in same unit and represents same phenomenon

Intuitively the easiest way seems to check nt>nt-1 and 1 if "yes" and 0 if "no", and make calculation on those numbers. Unfortunately I cant find any legitimate way to asses it. Are there any existing and recognized methods of measuring similarity in direction of change in two (or more) time series? Possibly more developed than converting numbers into 1 if grow and 0 if no grow.

Answer 1

if you form a transfer function ( regression on steroids !) between these two series , three anomalous points will be detected via Intervention Detection . This leads directly to adjusting 3 Y values (1,2 and 7). One could then correlate the adjusted Y and the original X to get a robust estimate of the cross-correlation which might be of interest to you as a more robust estimate of concordance.

It is not a measure of direction of change unless you simply compute the proportion of times that the adjusted Y and X move together.