goGARCHforecast-class: class: GO-GARCH Forecast Class
In rgarch: Flexible GARCH modelling in R

Description Objects from the Class Slots Extends Methods Note Author(s) References

Class for the GO-GARCH forecast.

The class is returned by calling the function gogarchforecast.

mforecast:: Multivariate forecast object.
uforecast:: Univariate forecast of class "uGARCHmultiforecast".

Class "mGARCHforecast", directly. Class "GARCHforecast", by class "mGARCHforecast", distance 2. Class "rGARCH", by class "mGARCHforecast", distance 3.

convolution: signature(object = "goGARCHforecast"):
function:
convolution(object, weights, fft.step = 0.01, fft.by = 0.0001, fft.support = c(-1, 1), support.method = c("user", "adaptive"), use.ff = TRUE, parallel = FALSE, parallel.control = list(pkg = c("multicore", "snowfall"), cores = 2), trace = 0,...)
The convolution method takes a goGARCHforecast object and a weights vector or matrix and calculates the weighted density. If a vector is given, it must be the same length as the number of assets, otherwise a matrix with row dimension equal to the row dimension of the filtered dataset (i.e. less any lags). In the case of the multivariate normal distribution, this simply returns the linear and quadratic transformation of the mean and covariance matrix, while in the multivariate affine NIG distribution this is based on the numerical inversion by FFT of the characteristic function. In that case, the “fft.step” option determines the stepsize for tuning the characteristic function inversion, “fft.by” determines the resolution for the equally spaced support given by “fft.support”, while the use of the “ff” package is recommended to avoid memory problems on some systems and is turned on via the “use.ff” option. The “support.method” option allows either a fixed support range to be given (option ‘user’), else an adaptive method is used based on the min and max of the assets at each point in time at the 0.00001 and 1-0.00001 quantiles. The range is equally spaced subject to the “fft.by” value but the returned object no longer makes of the “ff” package returning instead a list. Finally, the option for parallel computation is available, though it is far more efficient to use (in unix based systems only) using the “multicore” package than “snowfall”.
gportmoments: signature(object = "goGARCHforecast"):
function:
gportmoments(object, weights)
Calculates the first 4 portfolio moments using the geometric properties of the model, given a matrix of asset weights with row dimension equal to the row dimension of the filtered dataset (i.e. less any lags). The kurtosis is not returned for systems of dimensions greater than 11 because of the memory issues related to calculations on the co-kurtosis tensor.
rcokurt: signature(object = "goGARCHforecast"):
function:
rcokurt(object, from = 1, to = 1)
Returns the 'time-varying' NxN^4 cokurtosis tensor in array format and is limited to a dimensions of 11 assets. The “from” and “to” options indicate the time indices for which to return the arrays. Because of memory issues, this is limited to 100 indices.
rcoskew: signature(object = "goGARCHforecast"):
function:
rcoskew(object, from = 1, to = 1)
Returns the 'time-varying' NxN^3 coskewness tensor in array format. The “from” and “to” options indicate the time indices for which to return the arrays. Because of memory issues, this is limited to 100 indices.
rcov: signature(object = "goGARCHforecast"): Returns the time-varying NxN covariance matrix in array format.
rcor: signature(object = "goGARCHforecast"): Returns the time-varying NxN correlation matrix in array format.
show: signature(object = "goGARCHforecast"): Summary method for the forecast object.

The reference by Paolella (2007) contains more details on the algorithm for the characteristic function inversion via FFT. The de Athayde and Flores (2002) paper is the basis for the geometric properties of the higher moment tensors.
Forecasts are carried out on the time varying parameters of the factor distributions, and then scaled and transformed to those of the assets after adding back the mean forecast (which is either a constant or the VAR mean forecast).

Alexios Ghalanos

de Athayde, G.M. and Flores Jr, R.G. On Certain Geometric Aspects of Portfolio Optimisation with Higher Moments, 2002, mimeo.
Paolella, M.S.Intermediate Probability - A Computational Approach, 2007, Wiley-Interscience.

rgarch documentation built on May 2, 2019, 5:22 p.m.