Let's suppose that I have 6 variables with normal distributions and I don't know any values, the only thing I know is the covariance matrix. Can I construct tha matrix of fourth order moments using tha covariance matrix?

Actually, i cannot understand the structrure of this matrix. I have read that if tha covariance matrix has dimensions n x n,the 4th order moments matrix is n^2 x n^2. Is that correct?

Plus, for a normal distribution, tha third order moments are equal to zero, right? And I have this equation that gives the elements of the matrix I am looking for: (the M elements come from the covariance matrix)


Any help will be appreciated,