gonls: Non-linear least-squares estimation of matrix B
Description
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.
Usage
gonls(params, SSI)
Arguments
params
The initial values of the $vech(B)$.
SSI
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.
Value
fnumeric: The value of the target function.
encoding
latin1
concept
GARCH
GO-GARCH
Details
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
$Y = X Z^{-1}$.
References
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.