How to generate (and what is) the covariance matrix of coloured noises: Brown(red), Pink, Violet, Blue?
I see in https://en.wikipedia.org/wiki/White_noise#White_noise_vector
A necessary (but, in general, not sufficient) condition for statistical independence of two variables is that they be statistically uncorrelated; that is, their covariance is zero. Therefore, the covariance matrix R of the components of a white noise vector w with n elements must be an n by n diagonal matrix, where each diagonal element Rii is the variance of component wi; and the correlation matrix must be the n by n identity matrix.
Was looking into how to generate coloured noise series in the first place: Generate colors of noise in Python
But I don’t have enough domain knowledge to comprehend this and move to generate covariance matrix.
One way I think it could work is by generating a 2D coloured noise(How?) and then pass it to np.cov? But I am not sure if this is correct and this would end up being just an estimate.