Is there any quantitative technique available for estimating the magnitude of different curves.

Hello everyone, I have a question regarding time series data. Is there any quantitative technique available for estimating the magnitude of different curves. I have attached a figure for better understanding. By visual inspection, we can see that Time Series 2 and Time Series 4 have less variation in the data as compare to the other three curves. We should not consider the dc offset. Please help me in finding the right technique to quantify these time series data.

Thanks in advance, Irtaza

[Stephen23]

(max-min)/2 ?

[KSSV]

How about fft ?

[Syed Haider]

Stephen, but is there a name for this formula. I mean its just half of the range. KSSV,if i have to check it for thousands of curves then i think fft is computationally costly.

[Jan]

@Syed: You mean the half range? Then it is called "half range", for obvious reasons.

Answer 1

[Jan]

It depends on what you call "magnitude" or "variation". Perhaps:

Range    = max(x) - min(x);        % This is called "Range"
Int      = sum(abs(gradient(x)));  % Accumulated absolute derivatives
StdDev   = std(x);                 % Standard deviation
Variance = var(x);                 % Variance

FFT might be costly, but very useful. "Thousands" sounds like a work for parts of a second only.

[Syed Haider]

Thanks Simon. I know about range, std and var for sure :). But, is there any other way, for example, Euclidean Distance or any distance measure technique that deals with the cumulative sum of this time series data. Or may be any method that will calculate the length of the curvature in terms of its magnitude. Thanks,

[Jan]

@Syed: This is a really vague question. "Is there any other way?" Yes, of course there is. There are many ways. But as my trivial answers above show already: It would not be efficient if we post dozens of different method, when you are looking for something different. So it is your turn to specify, what you exactly want. Maybe spikes matter, maybe only the low frequencies of the signal. Maybe a phase shift is of interest, or not. Maybe similar wave forms matter, but the absolute scaling should be ignored. I could expand this list for the next 20 lines.

What do you need exactly?

[Syed Haider]

@Simon: I am sorry that I did not make the question clear. I need to differentiate between high wandering (more variation in amplitude) and low wandering (less variation in amplitude) of the time series data. I want to set certain threshold (based on some quantitative technique) that will help me in distinguishing between high wander and low wander time series data.

P.S i know i can use std, var or range but i am looking for any other technique.

Thanks.