# Comparing trends in 2 time series with different units, scales, directions of change?

I have two time series data as shown below in the figures. I want to compare if the rate of change is same in the both the line plots regardless of the direction of change (i.e increasing trend or decreasing trend). One of the series is increasing and the other is decreasing. Also, the units of measurement are different and the scales are also wildly different. The series in blue is in the range of -0.0001 to 0.0001 while the series in red is in the range of 0 to 50. Is there a method to do this ? Any suggestion would be really helpful for me.

Edit: Let me add some more context. If I inverse y axis of the series shown in red and plot over the series in blue with a separate y axis as shown in figure below I am able to say by intuition that both time series have a similar rate of change over the time period. Regardless of increasing/decreasing change and difference in scales. I want this intuitive inference to be represented by a numeric statistic. Is that possible?

• I presume you mean you want to compare the instantaneous rates of change. Just compute the correlation between the derivatives of the two functions. Ignore the sign if you don't care about direction. Commented Jun 7, 2018 at 0:25
• No. I dont want to compare instantaneous rates of change. I want to compare the amount of change both data have gone through for the whole time period being considered. To put an image, I want a single numerical value as a indicator of how similar the trend in the series are, regardless of direction of the trend, scales and units of the measurement in the series. Commented Jun 7, 2018 at 0:50