goGARCHfilter-class: class: GO-GARCH Filter Class

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

Description

Class for the GO-GARCH filter.

Objects from the Class

The class is returned by calling the function gogarchfilter and is mainly called by gogarchfit when the “out.sample” option is used.

Slots

mfilter:

Multivariate filter object.

ufilter:

Univariate multifilter of class "uGARCHmultifilter".

Extends

Class "mGARCHfilter", directly. Class "GARCHfilter", by class "mGARCHfilter", distance 2. Class "rGARCH", by class "mGARCHfilter", distance 3.

Methods

as.data.frame

signature(x = "goGARCHfilter"):
function:
as.data.frame(x, type = "A")
This returns four types of data.frame relating to the estimation of the independent components in the GO-GARCH model. Valid choices for “A” are “A” for the mixing matrix, “AA” for the unconditional covariance matrix, “U” for the rotational matrix and “K” for the whitening matrix. Note that for the latter, usually derived by an eigen or singular value decomposition, some ICA methods do return this and hence “U” cannot be calculated.

likelihood

signature(object = "goGARCHfilter"): The quasi log-likelihood of the model, which being an independent factor model is the sum of the univariate GARCH log-likelihoods plus a term for the mixing matrix.

coef

signature(object = "goGARCHfilter"): extraction of garch independent factor model coefficients.

fitted

signature(object = "goGARCHfilter"): Extracts the fitted values.

residuals

signature(object = "goGARCHfilter"): Extracts the mean equation residual values.

convolution

signature(object = "goGARCHfilter"):
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 goGARCHfilter 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”.

portmoments

signature(object = "goGARCHfilter"):
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 = "goGARCHfilter"):
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 = "goGARCHfilter") 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 = "goGARCHfilter"): Returns the time-varying NxN covariance matrix in array format.

rcor

signature(object = "goGARCHfilter"): Returns the time-varying NxN correlation matrix in array format.

show

signature(object = "goGARCHfilter"): Summary method for the filtered object.

Note

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.

Author(s)

Alexios Ghalanos

References

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.