Optimization

Quadratic Programming

Nonlinear Programming

Linear Least Squares

Function File: [beta, v, r] = gls (y, x, o)

Generalized least squares estimation for the multivariate model y = x * b + e with mean (e) = 0 and cov (vec (e)) = (s^2)*o, where Y is a T by p matrix, X is a T by k matrix, B is a k by p matrix, E is a T by p matrix, and O is a Tp by Tp matrix.

Each row of Y and X is an observation and each column a variable.

The return values beta, v, and r are defined as follows.

beta

The GLS estimator for b.

v

The GLS estimator for s^2.

r

The matrix of GLS residuals, r = y - x * beta.

Function File: [beta, sigma, r] = ols (y, x)

Ordinary least squares estimation for the multivariate model y = x*b + e with mean (e) = 0 and cov (vec (e)) = kron (s, I). where y is a t by p matrix, X is a t by k matrix, B is a k by p matrix, and e is a t by p matrix.

Each row of y and x is an observation and each column a variable.

The return values beta, sigma, and r are defined as follows.

beta

The OLS estimator for b, beta = pinv (x) * y, where pinv (x) denotes the pseudoinverse of x.

sigma

The OLS estimator for the matrix s,

sigma = (y-x*beta)' * (y-x*beta) / (t-rank(x))

r

The matrix of OLS residuals, r = y - x * beta.

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