Modes of variance of a time serie.

Good morning everyone! I will appreciate any help trying to run an EOF on a time series, not a matrix. The idea is to understand the modes of variability, like the first mode represent the x% of this real vector. So then, I can run an spectrum and find the frequencies that compose that mode. unfortunately, the emd(x) function did not export the variance of the modes, how much of that variance of the time serie is represented by the mode. maybe Im wrong on the way to understand modes on a time serie, probably there's a better way to understand this problem?, thanks to all.

Answer 1

[Shubham]

Hi Jorge,

To understand the modes of variability in a time series, you can use Empirical Mode Decomposition (EMD) to break it down into Intrinsic Mode Functions (IMFs), with each IMF representing a different mode of variability. While the emd function does not directly provide the variance explained by each mode, it can be calculated manually.

Here’s a clear way to approach this:

1. Empirical Mode Decomposition (EMD): Use the emd function to decompose your time series into IMFs.
2. Variance Calculation: Compute the variance of each IMF and compare it to the total variance of the time series to determine how much each mode contributes.
3. Spectral Analysis: Perform a Fourier Transform on each IMF to explore its frequency components.

Here' an example in MATLAB:

% Example time series data
time_series = randn(1000, 1);

% Perform EMD
imfs = emd(time_series);

% Calculate total variance
total_variance = var(time_series);

% Calculate variance explained by each mode (IMF)
variance_explained = var(imfs, 0, 1) / total_variance * 100;

% Display variance explained by each mode
for i = 1:length(variance_explained)
    fprintf('Mode %d explains %.2f%% of the variance\n', i, variance_explained(i));
end

% Perform spectral analysis using FFT
for i = 1:size(imfs, 2)
    Y = fft(imfs(:, i));
    P2 = abs(Y/length(time_series));
    P1 = P2(1:length(time_series)/2+1);
    P1(2:end-1) = 2*P1(2:end-1);
    f = (0:(length(time_series)/2))/length(time_series);
    
    figure;
    plot(f, P1);
    title(['Spectral Analysis of Mode ', num2str(i)]);
    xlabel('Frequency');
    ylabel('|P1(f)|');
end

For more information, refer to the following documentation links:

https://mathworks.com/help/releases/R2022b/signal/ref/emd.html

https://mathworks.com/help/releases/R2022b/matlab/ref/fft.html

Hope this helps.