Fit a repeated pattern

I have the following time series that i want to model.

The graph shows several 'events' that have a repeated pattern (i consider as an 'event' the data points between the long straight lines). I can fit each event (the parts between the straight lines) separately with a 3rd or 4th level polynomial but what i want is to create a continuous model to fit several plots like this one automatically.All events should have the same shape (the reason why they do not look exactly the same is because of some noise is added). Does anyone know how to create a model for this whole plot if i know the shape of one of those events? I have included the dataset in text files.

Answer 1

[Star Strider]

Getting the ensembles (data between the vertical lines) takes a bit of experimentation. It is then possible to put those data into a matrix of ensembles. Those data are then your to work with.

The Code —

x = load('x.txt');
y = load('y.txt');

[pks,locs] = findpeaks(-y, 'MinPeakHeight',-20, 'MinPeakDistance',100);     % Find Indices Of Vertical Lines

figure(1)
plot(x, y)
hold on
plot(x(locs), -pks, 'vr')
hold off

ensblen = min(diff(locs))-20;                                               % Length Of Each Vector, Eliminating Vertical Lines At Both Ends
ensbmtx = zeros(ensblen, numel(locs)-1);                                    % Preallocate
for k1 = 1:size(ensbmtx,2)
    ensbmtx(:,k1) = y(locs(k1)+[0:size(ensbmtx,1)-1]+15);                   % Create Ensemble
end

figure
ribbon((1:size(ensbmtx,1)), ensbmtx, 0.2, 'EdgeColor','w')                  % View Results (Optional)
grid on

The ‘ensbmtx’ (‘ensemble matrix’) result is (1886x10). Each vector is a column.

[Angela]

Thank you for the code. It really helps grouping the data. I was looking for a way to fit all the events at once. I know how to fit one of the events at a time (using a polynomial) but i want to find a formula that will fit all the events at once. Do you have an idea on how to do that? Thank you.

[Star Strider]

My pleasure.

It depends on how you want to fit them, and the polynomial you want to use. If you want to fit the mean of your data, this works:

indep = (0:size(ensbmtx,1)-1)'*x(1);
meanensb = mean(ensbmtx,2);
p = polyfit(indep, meanensb, 4);
f = polyval(p, indep);

figure
plot(indep, mean(ensbmtx,2), '.b')
hold on
plot(indep, f, '-r')
hold off
grid

A polynomial fit is likely not going to be meaningful if you actually want information from your data. A much better approach would be to use a mathematical model of the process that created your data, and then use it as your objective function in a nonlinear parameter estimation function (such as lsqcurvefit) to do the fit.

Answer 2

[Michiele Ogbagabir]

If you know the shape of one of those events, you may try implementing an iterative solution by wrapping around the x-interval of one such event. Lets say one such pattern spans an x-interval (0, 200). In this case you can modify your single-event-polynomial by passing it x % 200 instead of x and turn it into a model for this whole plot. But this would require prior knowledge of the pattern's intervals which may not be possible depending on what your application is.

[Angela]

Thank you for the suggestion. Is it possible to elaborate a little bit more or provide me with a sample code? Thank you for your time.