Building on early research by Bates and Granger (1969), the methodology of Newbold and Granger (1974) also extracts the combination weights from the estimated
mean squared prediction error matrix.Suppose $y_t$ is the variable of interest, there are $N$ not perfectly collinear predictors,
$f_t = (f_{1t}, \ldots, f_{Nt})'$, $\Sigma$ is the (positive definite)
mean squared prediction error matrix of $f_t$ and $e$ is an $N * 1$ vector of $(1, \ldots, 1)'$.
Their approach is a constrained minimization of the mean squared prediction error using the normalization condition $e'w = 1$.
This yields the following combination weights:
$$\mathbf{w}^{NG} = \frac{\Sigma^{-1}\mathbf{e}}{\mathbf{e}'\Sigma^{-1}\mathbf{e}}$$
The combined forecast is then obtained by:
$$\hat{y}_t = {\mathbf{f}_{t}}'\mathbf{w}^{NG}$$
While the method dates back to Newbold and Granger (1974), the variant of the method used here does not impose the prior restriction that $\Sigma$
is diagonal. This approach, called VC in Hsiao and Wan (2014), is a generalization of the original method.