# 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 |

`garchlist` |
List with optional elements passed to |

### 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`

.

### Author(s)

Bernhard Pfaff

### 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

1 2 3 4 5 6 7 8 9 |