time series comparison metric

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Angela
Angela 2018-12-10
评论： Angela 2018-12-11
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.
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Rik
Rik 2018-12-11
I was indeed thinking of a Fourier transform, but Chad's solution is probably better, as it is easier to explain.
Angela
Angela 2018-12-11
Thank you for your answer.

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Chad Greene
Chad Greene 2018-12-10
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)
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Angela
Angela 2018-12-11
Thank you. It worked. I got a nice reduction in the value std(d2_res).

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