Dear Ummara Razi ,

Granger causality (GC) is a popular method in causal linkage recovery and has been applied to various fields, such as economics and neuroscience. While the conventional Granger causality model is capable of identifying symmetrical causal relationships among variables, it is the asymmetric Granger causality that provides a more comprehensive perspective of the short- and long-term interactions between variables, which is of greater value for empirical study.

Article Wavelet Multiscale Granger Causality Analysis Based on State...

Article A MATLAB toolbox for Granger causal connectivity analysis

Regards,

Shafagat

Thank you so much Shafagat Mahmudova

• Preprocessing: Make sure your data is preprocessed appropriately for wavelet decomposition and Granger causality testing.
• Wavelet Selection: Choose the appropriate wavelet type and level of decomposition based on your specific application.
• Interpretation: Properly interpret the p-values to determine if there is significant Granger causality between the time series components.

% Load your data

data = load('your_data.mat');

x = data.x; % Time series x

y = data.y; % Time series y

% Wavelet Transformation

waveletType = 'db4'; % Daubechies wavelet

level = 5; % Level of decomposition

[cx, lx] = wavedec(x, level, waveletType);

[cy, ly] = wavedec(y, level, waveletType);

Ax = wrcoef('a', cx, lx, waveletType, level);

Dx = wrcoef('d', cx, lx, waveletType, level);

Ay = wrcoef('a', cy, ly, waveletType, level);

Dy = wrcoef('d', cy, ly, waveletType, level);

% Granger Causality Test

numLags = 2;

waveletComponentsX = [Ax, Dx];

waveletComponentsY = [Ay, Dy];

[h, pValue] = grangercause(waveletComponentsX, waveletComponentsY, numLags);

% Display results

if h == 1

fprintf('Reject the null hypothesis: Y Granger-causes X at the chosen lag.\n');

else

fprintf('Fail to reject the null hypothesis: Y does not Granger-cause X at the chosen lag.\n');

end

fprintf('P-value: %f\n', pValue);

Thank you so much Satya P. Singh . Really appreciate your response