gonls {gogarch}

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.

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}.

Value

f

numeric: The value of the target function.

Author(s)

Bernhard Pfaff

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.

See Also

gogarch