Let θ = (μ1, μ2, A1,1, A1,2, A2,2, ν), where μj is the mean of the jth variable, A1,1, A1,2, and A2,2 are the nonzero elements of A, and ν is the degrees-of-freedom parameter.
(a) What does the code A = chol(cov(Y)) do?
(b) Find θML, the MLE of θ.
(c) Find the Fisher information matrix for θ. (Hint: The Hessian is part of the object fit mvt. Also, the R function solve will invert a matrix.)
(d) Find the standard errors of the components of θML using the Fisher information matrix.
(e) Find the MLE of the covariance matrix of the returns.
(f ) Find the MLE of ρ, the correlation between the two returns (Y1 and Y2).