Hi Aneesh,
Exploiting correlation among time-scaled data with variable sizes can be challenging, especially when dealing with time series of different lengths. However, there are several techniques and approaches you can use in MATLAB to handle this:
1. Dynamic Time Warping (DTW):
DTW is a method that allows you to align two time series of different lengths by stretching or compressing them. This is particularly useful for finding similarities between time series that may vary in speed.
% Example using MATLAB's built-in function
ts1 = [1, 2, 3, 4, 5]; % Example time series 1
ts2 = [2, 3, 4]; % Example time series 2
% Calculate DTW distance
[dist, ix, iy] = dtw(ts1, ts2);
% Plot the alignment
figure;
dtwplot(ts1, ts2, ix, iy);
title(['DTW Distance: ', num2str(dist)]);
2. Resampling:
If the data is of variable size due to different sampling rates, you can resample the data to a common time grid.
% Resample time series to a common time grid
t1 = 0:0.1:1; % Original time vector for ts1
t2 = 0:0.2:1; % Original time vector for ts2
ts1_resampled = interp1(t1, ts1, linspace(0, 1, 100));
ts2_resampled = interp1(t2, ts2, linspace(0, 1, 100));
3. Cross-Correlation:
Cross-correlation can help identify lags between two time series. This method assumes that the time series are already aligned in terms of sampling rate.
% Compute cross-correlation
[c, lags] = xcorr(ts1_resampled, ts2_resampled);
% Plot the cross-correlation
figure;
plot(lags, c);
xlabel('Lag');
ylabel('Cross-correlation');
title('Cross-correlation between time series');
