This is the target function for estimating the matrix \(B\) by
non-linear least-squares. It is used in the estimation method
goest if method = "nls" is chosen.
gonls(params, SSI)The initial values of the \(vech(B)\).
A list with two elements, each a list itself, containing \(S_t = s_t s_t' - I_m\) and \(S_{t-1} = s_{t-1} s_{t-1}' - I_m\), respectively.
numeric: The value of the target function.
Boswijk and van der Weiden (2006) proposed the following criterion function:
$$ S(A) = \frac{1}{n} \sum_{t = 1}^n tr([s_t s_t' - I_m - B(s_{t-1} s_{t-1}' - I_m)B]^2) = S^*(B) $$
for retrieving the matrix \(U\). This matrix is the eigen vector matrix of \(B\). The linear map \(Z = P \Delta^{1/2} U\) and its inverse can then be computed for calculating the component matrix \(Y = X Z^{-1}\).
Boswijk, H. Peter and van der Weide, Roy (2006), Wake me up before you GO-GARCH, Tinbergen Institute Discussion Paper, TI 2006-079/4, University of Amsterdam and Tinbergen Institute.