# 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

 1 2 3 4 5 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.

### 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.

### Value

Returns an object of class GoGARCH.

Bernhard Pfaff

### References

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

Goinit, GoGARCH, Goestml, garchFit
 1 2 3 4 5 6 7 8 9 ## Not run: library(vars) data(VDW) var1 <- VAR(VDW, p = 1, type = "const") resid <- resid(var1) gin <- goinit(resid, scale = TRUE) gotheta(0.5, gin) ## End(Not run)