Thread Subject: weighted average time series

I am sure that what I want to do is simple in MATLAB, but my maths has totally failed me and Help is driving me round in circles. Can anyone help?

I have ten time series', all sampled over the same time interval, all trying to measure the same thing. All ten share a similar shape, but all of them show departures from it. All ten have a very different amplitude range, but they all start from 0.

In case my description isn't enough, the time series' look like this (ignore the red one):
http://www.pbase.com/dormant/image/122549911

I want to combine them together to construct a weighted-average time series. So I need to determine one average time series and ten weights.

I thought this would be a least-squares problem, but I can't seem to get it in the right form.

How about normalizing all of them to have a maximum value of 1? You can obtain a set of weights this way, but I don't know if this simple solution would work for you.

Best.


"dormant" <rod.stewart@uwiseismic.com> wrote in message <hn0skl$ppc$1@fred.mathworks.com>...
> I am sure that what I want to do is simple in MATLAB, but my maths has totally failed me and Help is driving me round in circles. Can anyone help?
>
> I have ten time series', all sampled over the same time interval, all trying to measure the same thing. All ten share a similar shape, but all of them show departures from it. All ten have a very different amplitude range, but they all start from 0.
>
> In case my description isn't enough, the time series' look like this (ignore the red one):
> http://www.pbase.com/dormant/image/122549911
>
> I want to combine them together to construct a weighted-average time series. So I need to determine one average time series and ten weights.
>
> I thought this would be a least-squares problem, but I can't seem to get it in the right form.

Or, instead of normalizing to the max value, you could normalize them
by the area under the curve. Depends on what you want to do. The
normalization method you select might depend on what gave rise to the
different amplitudes, plus the noise spectrum. If it's just a gain
difference, then you should normalize to the max but the problem is
the max could be a noise spike, so you might have to do some noise
reduction and then divide by the max.

Thanks for the suggestions, some of which I tried already.

To answer one question. The signals I am discussing are not the same signal plus different noise in each time series. The signal is subtly different in each time series, and I am trying to quantify these differences. There is also noise present, but that can't be removed by any processing.

On Mar 9, 1:06 pm, "dormant" <rod.stew...@uwiseismic.com> wrote:
> Thanks for the suggestions, some of which I tried already.
>
> To answer one question. The signals I am discussing are not the same signal plus different noise in each time series. The signal is subtly different in each time series, and I am trying to quantify these differences. There is also noise present, but that can't be removed by any processing.
-----------------------------------------------------------------------------
So you have no noise and the signals are different because they really
are different. And you are "trying to quantify the differences." So,
in the absence of any other information, I'd say that you just simply
subtract the signals to get the differences. If that's not right,
then say why.

I think the amplitude is one obvious difference, but I'm assuming you mean the shape as well?

Honestly, normalizing seems the best way, the question is how. Normalize so the max = 1, or the sum = 1, is probably right. But without knowledge of how the signal works (is it "adding", hence a gain problem, like ImageAnalyst says? or is it multiplying, so we need to consider a log scale?) The picture doesn't tell enough (actually, it does if I measure, but not gonna) to know.

You say you tried some things, but no cigar? Did you try normalizing? To simplify it, if you like, you could use "buckets," since what you have is basically a histogram. If not a histogram exactly, then you could certainly treat it like one.

Of course, once they are all normalized, you would probably be taking differences, just like ImageAnalyst says. I can't really see why normalizing and then difference wouldn't work, simple as it may seem.

"dormant" <rod.stewart@uwiseismic.com> wrote in message <hn0skl$ppc$1@fred.mathworks.com>...
> I am sure that what I want to do is simple in MATLAB, but my maths has totally failed me and Help is driving me round in circles. Can anyone help?
>
> I have ten time series', all sampled over the same time interval, all trying to measure the same thing. All ten share a similar shape, but all of them show departures from it. All ten have a very different amplitude range, but they all start from 0.
>
> In case my description isn't enough, the time series' look like this (ignore the red one):
> http://www.pbase.com/dormant/image/122549911
>
> I want to combine them together to construct a weighted-average time series. So I need to determine one average time series and ten weights.
>
> I thought this would be a least-squares problem, but I can't seem to get it in the right form.