Fit a repeated pattern
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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.
Star Strider on 27 Jun 2018
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
plot(x(locs), -pks, 'vr')
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
ribbon((1:size(ensbmtx,1)), ensbmtx, 0.2, 'EdgeColor','w') % View Results (Optional)
The ‘ensbmtx’ (‘ensemble matrix’) result is (1886x10). Each vector is a column.
More Answers (1)
Michiele Ogbagabir on 27 Jun 2018
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.