## time series comparison metric

### Angela (view profile)

on 10 Dec 2018
Latest activity Commented on by Angela

### Angela (view profile)

on 11 Dec 2018

I have two sets of time series (attached in text) and i want to compare them in a quantitative way.
My interest is in showing that the second series is more smooth than the first because
that is what it looks like visually. I am looking for a metric that shows that smoothness.

Show 1 older comment
Angela

### Angela (view profile)

on 10 Dec 2018
What do you mean by magnitude of higher frequency changes? FFT or something else?
I thought of using the variance but that does not seem appropriate because a straight line can have a big variance and still be smooth. I do not know any other metric.
Rik

### Rik (view profile)

on 11 Dec 2018
I was indeed thinking of a Fourier transform, but Chad's solution is probably better, as it is easier to explain.
Angela

on 11 Dec 2018

### Tags

on 10 Dec 2018

The simplest way is just to compare the standard deviations of each signal:
st1 = std(d1);
st2 = std(d2);
Although that approach might be dominated by low frequency variability. So you could go one step fancier just analyze the residuals after removing the moving mean. Pick some window for the moving mean (I'm using 500 below) and then compare the standard deviations:
d1_res = d1 - movmean(d1,500);
d2_res = d2 - movmean(d2,500);
std(d1_res)
std(d2_res)

Angela

### Angela (view profile)

on 11 Dec 2018
Thank you. It worked. I got a nice reduction in the value std(d2_res).