gogarch (version 0.7-0)

gotheta: Creates an object of class GoGARCH based on Euler angles

Description

This function returns an object of class GoGARCH based on an input vector of Euler angles.

Usage

gotheta(theta, object, garchlist = list(init.rec = "mci", delta = 2,
skew = 1, shape = 4, cond.dist = "norm", include.mean = FALSE,
include.delta = NULL, include.skew = NULL, include.shape = NULL,
leverage = NULL, trace = FALSE, algorithm = "nlminb", hessian = "ropt",
control = list(), title = NULL, description = NULL))

Arguments

theta

Vector of Euler angles.

object

An object of formal class Goinit or an extension thereof.

garchlist

List with optional elements passed to garchFit.

Value

• Returns an object of class GoGARCH.

encoding

latin1

concept

• GO-GARCH
• Euler angles

Details

In a first step the orthogonal matrix $U$ is computed as the product of rotation matrices given the vector theta of Euler angles with the function UprodR. The linear map $Z$ is computed next as $Z = P D^{\frac{1}{2}} U'$. The unobserved components $Y$ are calculated as $Y = X Z^{-1}$. These are then utilized in the estimation of the univariate GARCH models according to object@garchf. The conditional variance/covariance matrices are calculated according to $V_t = Z H_t Z'$ whereby $H_t$ signifies a matrix with the conditional variances of the unvariate GARCH models on its diagonal.

References

Van der Weide, Roy (2002), GO-GARCH: A Multivariate Generalized Orthogonal GARCH Model, Journal of Applied Econometrics, 17(5), 549 -- 564.

See Also

Goinit, GoGARCH, Goestml, garchFit

Examples

library(vars)
data(VDW)
var1 <- VAR(VDW, p = 1, type = "const")
resid <- resid(var1)
gin <- goinit(resid, scale = TRUE)
gotheta(0.5, gin)