# How to detect changes in amplitude?

I have timeseries like this:

as you can see there are changes regarding the amplitude. Is there a test to check this kind of changes?

Important annotations:

1. I do not know if the series have changes in amplitude
2. If there is a change in amplitude I do not know the point of the change
3. The changes can be more then ONE (but I only need to know if there is a change in amplitude, for my tests the numbers of changes is not important)
4. As you can see the means are common
5. I do not have groups I have series in a numeric vector (R vector), I only subdivided the above series in three groups to show the three changes in amplidute, but it is very obvious.
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Could it be helpful to rephrase this as a 'change in variance' rather than a 'change in amplitude'? –  silvialiverani Jan 9 '12 at 16:19
Perhaps a short-term sum (plain or weighted) of the magnitudes such as $$X_n = \sum_{i=0}^k |x_{n-i}|~~\text{or}~~ X_n = \sum_{i=0}^k a_i|x_{n-i}|$$ where the $a_i$'s are a decreasing sequence used to discount past values, followed by binning the sums $X_n$ might work. You might also want to ask this question on dsp.SE where also some people have experience with time series –  Dilip Sarwate Jan 9 '12 at 16:31
@silvialiverani no, because maybe the variance could be the same, in the chart above yes, the variance changes...but the chart can have waves with different amplitudes. –  Dail Jan 9 '12 at 16:39
@DilipSarwate is there not a method (in R) to apply this kind of check? –  Dail Jan 9 '12 at 16:39
Any changepoint method (search the change-point tag) will do the trick when applied to the cumulative sums of absolute values of the data. The nice thing about such an approach is that it is not purely ad hoc: it will enjoy all the properties of the changepoint detector you choose. –  whuber Jan 9 '12 at 18:06

Try package ‘changepoint’, described here:

http://www.lancs.ac.uk/~killick/Pub/KillickEckley2011.pdf

It is able to detected changepoints in both mean and variance.

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+1 You ought to consider expanding this answer in light of the comment thread below the original question, because the OP wonders about applying a changepoint method near the ends of the series. –  whuber Jan 17 '12 at 23:11