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Hi I have a fairly simple question

Say I have a covariance matrix C that describes the noise in some data series D, including correlations between different data points (so just a general correlated gaussian).

I thought that if i wanted to work out the theoretical RMS of the signal such a matrix describes i could just use the square root of the diagonal elements, however, if i generate 100000 realisations of noise described by my covariance matrix by taking the cholesky decomposition and using that to generate my data series, i get an rms of 1.23508e-07 however the square root of all the diagonal elements of the covariance matrix are 2.12019e-07 and i don't understand where the offset is coming from.

How should i go about getting the theoretical rms from the covariance matrix?

Cheers

Jim Wolson
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1 Answers1

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Every covariance matrix can be diagonalized by some orthogonal matrix in such a way that the diagonal entries are nonnegative. Do that and use the sum of squares of the resulting diagonal entries.

Michael Hardy
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  • do you mean like eg, take the SVD of the covariance matrix and use the diagonal part of the decomposition? – Jim Wolson Jun 07 '13 at 23:27
  • Yes. If using diagonal entries would be appropriate if the observations were uncorrelated, then that's the way to do this. – Michael Hardy Jun 08 '13 at 15:23