The rmgarch package

Description

The rmgarch provides a selection of multivariate GARCH models with methods for fitting, filtering, forecasting and simulation with additional support functions for working with the returned objects. At present, the Generalized Orthogonal GARCH using Independent Components Analysis (ICA) and Dynamic Conditional Correlation (with multivariate Normal, Laplace and Student distributions) models are fully implemented, with methods for spec, fit, filter, forecast, simulation, and rolling estimation and forecasting, as well as specialized functions to calculate and work with the weighted portfolio conditional density. The Copula-GARCH model is also implemented with the multivariate Normal and Student distributions, with dynamic (DCC) and static estimation of the correlation.

Details

The main package functionality, currently supports the GO-GARCH with ICA method, and is available through the gogarchspec, gogarchfit, gogarchfilter, gogarchforecast, gogarchsim and gogarchroll functions. The DCC with multivariate Normal, Laplace and Student distributions is also supported with the main functionality in dccspec, dccfit, dccfilter, dccforecast, dccsim and dccroll. The Normal and Student Copula-GARCH, with dynamic or static correlation, is implemented with the main functionality in cgarchspec, cgarchfit, cgarchfilter, and cgarchsim. Usual extractor and support methods for the multivariate GARCH models are documented in the class of the returned objects.
.

How to cite this package

Whenever using this package, please cite as

@Manual{Ghalanos_2014,
 author       = {Alexios Galanos},
 title        = {{rmgarch}: Multivariate GARCH models.},
 year         = {2019},
 note 	      = {R package version 1.3-6.}}

License

The releases of this package is licensed under GPL version 3.

Author(s)

Alexios Galanos

References

Bollerslev, T. 1990, Modelling the coherence in short-run nominal exchange rates: a multivariate generalized ARCH model, The Review of Economics and Statistics, 72(3), 498–505.
Broda, S.A. and Paolella, M.S. 2009, CHICAGO: A Fast and Accurate Method for Portfolio Risk Calculation, Journal of Financial Econometrics 7(4), 412–436 .
Cappiello, L., Engle, R.F. and Sheppard, K. 2006, Asymmetric dynamics in the correlations of global equity and bond returns, Journal of Financial Econometrics 4, 537–572.
Croux, C. and Joossens, K. 2008, Robust estimation of the vector autoregressive model by a least trimmed squares procedure, COMPSTAT, 489–501.
Chen, Y., Hardle, W., and Spokoiny, V. 2010, GHICA - Risk analysis with GH distributions and independent components, Journal of Empirical Finance, 17(2), 255–269.
de Athayde, G.M. and Flores Jr, R.G. 2002, On Certain Geometric Aspects of Portfolio Optimisation with Higher Moments, mimeo.
Engle, R.F. 2002, Dynamic conditional correlation, Journal of Business and Economic Statistics 20, 339–350.
Engle, R.F. and Sheppard, K. 2001, Theoretical and empirical properties of dynamic conditional correlation multivariate GARCH, NBER Working Paper.
Genest, C., Ghoudi, K. and Rivest, L. 1995, A semiparametric estimation procedure of dependence parameters in multivariate families of distributions, Biometrika, 82, 543–552.
Ghalanos, A., Rossi, E., and Urga, G. (2014). Independent Factor Autoregressive Conditional Density Model, Econometric Reviews.
Paolella, M.S. 2007, Intermediate Probability - A Computational Approach, Wiley-Interscience.
Schmidt, R., Hrycej, T. and Stutzle 2006, Multivariate distribution models with generalized hyperbolic margins, Computational Statistics \& Data Analysis 50(8), 2065–2096.

class: DCC Filter Class

Description

The class is returned by calling the function dccfilter.

Slots

mfilter:

Object of class "vector". Multivariate filter list.

model:

Object of class "vector". Model specification list.

Extends

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

Methods

coef

signature(object = "DCCfilter") The coefficient vector (see note).

likelihood

signature(object = "DCCfilter"): The joint likelihood.

rshape

signature(object = "DCCfilter"): The multivariate distribution shape parameter(s).

rskew

signature(object = "DCCfilter"): The multivariate distribution skew parameter(s).

fitted

signature(object = "DCCfilter"): The filtered conditional mean xts object.

sigma

signature(object = "DCCfilter"): The filtered conditional sigma xts object.

residuals

signature(object = "DCCfilter"): The filtered conditional mean residuals xts object.

plot

signature(x = "DCCfilter", y = "missing"): Plot method, given additional arguments ‘series’ and ‘which’.

infocriteria

signature(object = "DCCfilter"): Information criteria.

rcor

signature(object = "DCCfilter"): The filtered dynamic conditional correlation array given additional argument ‘type’ (either “R” for the correlation else will return the “Q” matrix). The third dimension label of the array gives the time index (from which it is then possible to construct pairwise xts objects for example). A further argument ‘output’ allows to switch between “array” and “matrix” returned object.

rcov

signature(object = "DCCfilter"): The filtered dynamic conditional covariance array. The third dimension label of the array gives the time index (from which it is then possible to construct pairwise xts objects for example). A further argument ‘output’ allows to switch between “array” and “matrix” returned object.

show

signature(object = "DCCfilter"): Summary.

nisurface

signature(object = "DCCfilter"): The news impact surface plot given additional arguments ‘type’ with either “cov” or “cor” (for the covariance and correlation news impact respectively), ‘pair’ denoting the asset pair (defaults to c(1,2)), ‘plot’ (logical) and ‘plot.type’ with a choice of either “surface” or “contour”.

Note

The ‘coef’ method takes additional argument ‘type’ with valid values ‘garch’ for the univariate garch parameters, ‘dcc’ for the second stage dcc parameters and by default returns all the parameters in a named vector.

Author(s)

Alexios Galanos

References

Engle, R.F. and Sheppard, K. 2001, Theoretical and empirical properties of dynamic conditional correlation multivariate GARCH, NBER Working Paper.

class: DCC Fit Class

Description

The class is returned by calling the function dccfit.

Slots

mfit:

Object of class "vector" Multivariate filter list.

model:

Object of class "vector" Model specification list.

Extends

Class "mGARCHfit", directly. Class "GARCHfit", by class "mGARCHfit", distance 2. Class "rGARCH", by class "mGARCHfit", distance 3.

Methods

coef

signature(object = "DCCfit") The coefficient vector (see note).

likelihood

signature(object = "DCCfit"): The joint likelihood.

rshape

signature(object = "DCCfit"): The multivariate distribution shape parameter(s).

rskew

signature(object = "DCCfit"): The multivariate distribution skew parameter(s).

fitted

signature(object = "DCCfit"): The fitted conditional mean xts object.

sigma

signature(object = "DCCfit"): The fitted conditional GARCH sigma xts object.

residuals

signature(object = "DCCfit"): The fitted conditional mean residuals xts object.

plot

signature(x = "DCCfit", y = "missing"): Plot method, given additional arguments ‘series’ and ‘which’.

infocriteria

signature(object = "DCCfit"): Information criteria.

rcor

signature(object = "DCCfit"): The fitted dynamic conditional correlation array given additional arguments ‘type’ (either “R” for the correlation else will return the Q matrix). The third dimension label of the array gives the time index (from which it is then possible to construct pairwise xts objects for example). The argument ‘output’ can be either “array” (default) or “matrix” in which case the array is flattened and the lower diagonal time varying values are returned (and if a date exists, then the returned object is of class xts).

rcov

signature(object = "DCCfit"): The fitted dynamic conditional covariance array. The third dimension label of the array gives the time index (from which it is then possible to construct pairwise xts objects for example). The argument ‘output’ can be either “array” (default) or “matrix” in which case the array is flattened and the lower and main diagonal time varying values are returned (and if a date exists, then the returned object is of class xts).

show

signature(object = "DCCfit"): Summary.

nisurface

signature(object = "DCCfit"): The news impact surface plot given additional arguments ‘type’ with either “cov” or “cor” (for the covariance and correlation news impact respectively), ‘pair’ (defaults to c(1,2)), ‘plot’ (logical) and ‘plot.type’ with a choice of either “surface” or “contour”.

Note

The ‘coef’ method takes additional argument ‘type’ with valid values ‘garch’ for the univariate garch parameters, ‘dcc’ for the second stage dcc parameters and by default returns all the parameters in a named vector.

Author(s)

Alexios Galanos

References

Engle, R.F. and Sheppard, K. 2001, Theoretical and empirical properties of dynamic conditional correlation multivariate GARCH, NBER Working Paper.

class: DCC Forecast Class

Description

The class is returned by calling the function dccforecast.

Slots

mforecast:

Object of class "vector" Multivariate forecast list.

model:

Object of class "vector" Model specification list.

Extends

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

Methods

rshape

signature(object = "DCCforecast"): The multivariate distribution shape parameter(s).

rskew

signature(object = "DCCforecast"): The multivariate distribution skew parameter(s).

fitted

signature(object = "DCCforecast"): The conditional mean forecast array of dimensions n.ahead x n.assets by (n.roll+1). The thirds dimension of the array has the T+0 index label.

sigma

signature(object = "DCCforecast"): The conditional sigma forecast array of dimensions n.ahead x n.assets by (n.roll+1). The thirds dimension of the array has the T+0 index label.

plot

signature(x = "DCCforecast", y = "missing"): Plot method, given additional arguments ‘series’ and ‘which’.

rcor

signature(object = "DCCforecast"): The forecast dynamic conditional correlation list of arrays of length (n.roll+1), with each array of dimensions n.assets x n.assets x n.ahead. The method takes on one additional argument ‘type’ (either “R” for the correlation else will return the DCC Q matrix). A further argument ‘output’ allows to switch between “array” and “matrix” returned object.

rcov

signature(object = "DCCforecast"): The forecast dynamic conditional correlation list of arrays of length (n.roll+1), with each array of dimensions n.assets x n.assets x n.ahead. A further argument ‘output’ allows to switch between “array” and “matrix” returned object.

show

signature(object = "DCCforecast"): Summary.

Author(s)

Alexios Galanos

References

Engle, R.F. and Sheppard, K. 2001, Theoretical and empirical properties of dynamic conditional correlation multivariate GARCH, NBER Working Paper.

class: DCC Roll Class

Description

The class is returned by calling the function dccroll.

Slots

mforecast:

Object of class "vector" Multivariate forecast list.

model:

Object of class "vector" Model specification list.

Extends

Class "mGARCHroll", directly. Class "GARCHroll", by class "mGARCHroll", distance 2. Class "rGARCH", by class "mGARCHroll", distance 3.

Methods

coef

signature(object = "DCCroll"): The coefficient array across the rolling estimations with a T+0 3rd dimension index label.

fitted

signature(object = "DCCroll"): The conditional mean forecast xts object (with the actual T+i forecast dates as index).

likelihood

signature(object = "DCCroll"): The log-likelihood across rolling estimations.

plot

signature(x = "DCCroll", y = "missing"): Plot method, given additional arguments ‘series’ and ‘which’.

rcor

signature(object = "DCCroll"): The forecast dynamic conditional correlation array, with the T+i forecast index in the 3rd dimension label. Optional argument ‘type’ determines whether to return “R” for the correlation else will the DCC Q matrix. A further argument ‘output’ allows to switch between “array” and “matrix” returned object.

rcov

signature(object = "DCCroll"): The forecast dynamic conditional covariance array, with the T+i forecast index in the 3rd dimension label. A further argument ‘output’ allows to switch between “array” and “matrix” returned object.

rshape

signature(object = "DCCroll"): The multivariate distribution shape parameter(s).

rskew

signature(object = "DCCroll"): The multivariate distribution skew parameter(s).

show

signature(object = "DCCroll"): Summary.

sigma

signature(object = "DCCroll"): The conditional sigma forecast xts object (with the actual T+i forecast dates as index).

Author(s)

Alexios Galanos

References

Engle, R.F. and Sheppard, K. 2001, Theoretical and empirical properties of dynamic conditional correlation multivariate GARCH, NBER Working Paper.

class: DCC Forecast Class

Description

The class is returned by calling the function dccsim.

Slots

msim:

Object of class "vector" Multivariate simulation list.

model:

Object of class "vector" Model specification list.

Extends

Class "mGARCHsim", directly. Class "GARCHsim", by class "mGARCHsim", distance 2. Class "rGARCH", by class "mGARCHsim", distance 3.

Methods

fitted

signature(object = "DCCsim"): The conditional mean simulated data matrix given additional argument ‘sim’ denoting the simulation run (m.sim) to return values for.

rcor

signature(object = "DCCsim"): The simulated dynamic conditional correlation array given additional arguments ‘sim’ denoting the simulation run (m.sim) to return values for, and ‘type’ (either “R” for the correlation else will return the Q matrix). A further argument ‘output’ allows to switch between “array” and “matrix” returned object.

rcov

signature(object = "DCCsim"): The simulated dynamic conditional covariance array given additional argument ‘sim’ denoting the simulation run (m.sim) to return values for. A further argument ‘output’ allows to switch between “array” and “matrix” returned object.

sigma

signature(object = "DCCsim"): The univariate simulated conditional sigma matrix given additional argument ‘sim’ (m.sim) denoting the simulation run to return values for.

show

signature(object = "DCCsim"): Summary.

Author(s)

Alexios Galanos

References

Engle, R.F. and Sheppard, K. 2001, Theoretical and empirical properties of dynamic conditional correlation multivariate GARCH, NBER Working Paper.

class: DCC Specification Class

Description

The class is returned by calling the function dccspec.

Slots

model:

Object of class "vector" The multivariate model specification list.

umodel:

Object of class "vector" The univariate model specification list.

Extends

Class "mGARCHspec", directly. Class "GARCHspec", by class "mGARCHspec", distance 2. Class "rGARCH", by class "mGARCHspec", distance 3.

Methods

setfixed<-

signature(object = "DCCspec", value = "vector"): Set fixed second stage parameters.

setstart<-

signature(object = "DCCspec", value = "vector"): Set starting second stage parameters.

show

signature(object = "DCCspec"): Summary.

Note

The ‘umodel’ list is absorbed into the ‘model’ list in all other DCC classes.

Author(s)

Alexios Galanos

References

Croux, C. and Joossens, K. 2008, Robust estimation of the vector autoregressive model by a least trimmed squares procedure, COMPSTAT, 489–501.
Cappiello, L., Engle, R.F. and Sheppard, K. 2006, Asymmetric dynamics in the correlations of global equity and bond returns, Journal of Financial Econometrics 4, 537–572.
Engle, R.F. and Sheppard, K. 2001, Theoretical and empirical properties of dynamic conditional correlation multivariate GARCH, NBER Working Paper.

Engle and Sheppard Test of Dynamic Correlation

Description

A test of non-constant correlation based on Engle and Sheppard (2001).

Usage

DCCtest(Data, garchOrder = c(1,1), n.lags = 1, solver = "solnp", 
solver.control = list(), cluster = NULL, Z = NULL)

Arguments

Details

The test effectively equates to estimating a multivariate dataset using the Constant Conditional Correlation (CCC) model of Bollerslev (1990) and after which the standardized residuals (standardized by the symmetric square root decomposition of the estimated constant correlation matrix) should be i.i.d. with covariance the identity matrix. Testing for this can be done using a series of artificial regressions on the outer and lagged product of these residuals and a constant. In the rmgarch package, the CCC model is calculated using a static GARCH copula (Normal) model.

Value

A list with the proposed Null hypothesis (H0), the test statistic and its p-value.

Author(s)

Alexios Galanos

References

Bollerslev, T. 1990, Modelling the coherence in short-run nominal exchange rates: a multivariate generalized ARCH model, The Review of Economics and Statistics, 72(3), 498–505.
Engle, R.F. and Sheppard, K. 2001, Theoretical and empirical properties of dynamic conditional correlation multivariate GARCH, NBER Working Paper.

class: Copula Filter Class

Description

The class is returned by calling the function cgarchfilter.

Slots

mfilter:

Object of class "vector" Multivariate filter list.

model:

Object of class "vector" Model specification list.

Extends

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

Methods

coef

signature(object = "cGARCHfilter"): The coefficient vector (see note).

fitted

signature(object = "cGARCHfilter"): The conditional mean filtered data (xts object).

likelihood

signature(object = "cGARCHfilter"): The joint likelihood.

rcor

signature(object = "cGARCHfilter"): The conditional correlation array with third dimension labels the time index.

rcov

signature(object = "cGARCHfilter"): The conditional covariance array with third dimension labels the time index.

residuals

signature(object = "cGARCHfilter"): The model residuals (xts object).

show

signature(object = "cGARCHfilter"): Summary.

sigma

signature(object = "cGARCHfilter"): The model conditional sigma (xts object).

rshape

signature(object = "cGARCHfilter"): The multivariate distribution shape parameter(s).

rskew

signature(object = "cGARCHfilter"): The multivariate distribution skew parameter(s).

Note

The ‘coef’ method takes additional argument ‘type’ with valid values ‘garch’ for the garch parameters, ‘dcc’ for the second stage parameters and by default returns all the parameters in a named vector.

Author(s)

Alexios Galanos

References

Joe, H. Multivariate Models and Dependence Concepts, 1997, Chapman \& Hall, London.
Genest, C., Ghoudi, K. and Rivest, L. A semiparametric estimation procedure of dependence parameters in multivariate families of distributions, 1995, Biometrika, 82, 543-552.

class: Copula Fit Class

Description

The class is returned by calling the function cgarchfit.

Slots

mfit:

Object of class "vector" Multivariate fit list.

model:

Object of class "vector" Model specification list.

Extends

Class "mGARCHfit", directly. Class "GARCHfit", by class "mGARCHfit", distance 2. Class "rGARCH", by class "mGARCHfit", distance 3.

Methods

coef

signature(object = "cGARCHfit"): The coefficient vector (see note).

fitted

signature(object = "cGARCHfit"): The conditional mean fitted data (xts object).

likelihood

signature(object = "cGARCHfit"): The joint likelihood.

rcor

signature(object = "cGARCHfit"): The conditional correlation array with third dimension labels the time index. A further argument ‘output’ allows to switch between “array” and “matrix” returned object.

rcov

signature(object = "cGARCHfit"): The conditional covariance array with third dimension labels the time index. A further argument ‘output’ allows to switch between “array” and “matrix” returned object.

rshape

signature(object = "cGARCHfit"): The multivariate distribution shape parameter(s).

rskew

signature(object = "cGARCHfit"): The multivariate distribution skew parameter(s).

residuals

signature(object = "cGARCHfit"): The model residuals (xts object).

show

signature(object = "cGARCHfit"): Summary.

sigma

signature(object = "cGARCHfit"): The model conditional sigma (xts object).

Note

The ‘coef’ method takes additional argument ‘type’ with valid values ‘garch’ for the garch parameters, ‘dcc’ for the second stage parameters and by default returns all the parameters in a named vector.

Author(s)

Alexios Galanos

References

Joe, H. Multivariate Models and Dependence Concepts, 1997, Chapman \& Hall, London.
Genest, C., Ghoudi, K. and Rivest, L. A semiparametric estimation procedure of dependence parameters in multivariate families of distributions, 1995, Biometrika, 82, 543-552.

class: Copula Simulation Class

Description

The class is returned by calling the function cgarchsim.

Slots

msim:

Object of class "vector" Multivariate simulation list.

model:

Object of class "vector" Model specification list.

Extends

Class "mGARCHsim", directly. Class "GARCHsim", by class "mGARCHsim", distance 2. Class "rGARCH", by class "mGARCHsim", distance 3.

Methods

fitted

signature(object = "cGARCHsim"): The simulated conditional returns matrix given. Takes optional argument “sim” indicating the simulation run to return (from the m.sim option of the cgarchsim method.

sigma

signature(object = "cGARCHfit"): The simulated conditional sigma matrix given. Takes optional argument “sim” indicating the simulation run to return (from the m.sim option of the cgarchsim method.

rcor

signature(object = "cGARCHsim"): The simulated conditional correlation array (for DCC type). Takes optional argument “sim” indicating the simulation run to return (from the m.sim option of the cgarchsim method. A further argument ‘output’ allows to switch between “array” and “matrix” returned object.

rcov

signature(object = "cGARCHsim"): The simulated conditional covariance array. Takes optional argument “sim” indicating the simulation run to return (from the m.sim option of the cgarchsim method. A further argument ‘output’ allows to switch between “array” and “matrix” returned object.

show

signature(object = "cGARCHsim"): Summary.

Author(s)

Alexios Galanos

References

Joe, H. Multivariate Models and Dependence Concepts, 1997, Chapman \& Hall, London.
Genest, C., Ghoudi, K. and Rivest, L. A semiparametric estimation procedure of dependence parameters in multivariate families of distributions, 1995, Biometrika, 82, 543-552.

class: Copula Specification Class

Description

The class is returned by calling the function cgarchspec.

Slots

model:

Object of class "vector" The multivariate model specification

umodel:

Object of class "uGARCHmultispec" The univariate model specification.

Extends

Class "mGARCHspec", directly. Class "GARCHspec", by class "mGARCHspec", distance 2. Class "rGARCH", by class "mGARCHspec", distance 3.

Methods

show

signature(object = "cGARCHspec"): Summary.

setfixed<-

signature(object = "cGARCHspec", value = "vector"): Set fixed second stage parameters.

setstart<-

signature(object = "cGARCHspec", value = "vector"): Set starting second stage parameters.

Author(s)

Alexios Galanos

References

Joe, H. Multivariate Models and Dependence Concepts, 1997, Chapman \& Hall, London.
Genest, C., Ghoudi, K. and Rivest, L. A semiparametric estimation procedure of dependence parameters in multivariate families of distributions, 1995, Biometrika, 82, 543-552.

function: Copula-GARCH Filter

Description

Method for creating a Copula-GARCH filter object.

Usage

cgarchfilter(spec, data, out.sample = 0, filter.control = list(n.old = NULL), 
spd.control = list(lower = 0.1, upper = 0.9, type = "pwm", kernel = "epanech"), 
cluster = NULL, varcoef = NULL, realizedVol = NULL, ...)  

Arguments

Value

A cGARCHfilter object containing details of the Copula-GARCH filter and sharing most of the methods of the cGARCHfit class.

Note

The ‘n.old’ option in the filter.control argument is key in replicating conditions of the original fit. That is, if you want to filter a dataset consisting of an expanded dataset (versus the original used in fitting), but want to use the same assumptions as the original dataset then the ‘n.old’ argument denoting the original number of data points passed to the cgarchfit function must be provided. This is then used to ensure that some calculations which make use of the full dataset (unconditional starting values for the garch filtering, the dcc model and the copula transformation methods) only use the first ‘n.old’ points thus replicating the original conditions making filtering appropriate for rolling 1-ahead forecasting.
For extensive examples look in the ‘rmgarch.tests’ folder.

Author(s)

Alexios Galanos

function: Copula-GARCH Fit

Description

Method for creating a Copula-GARCH fit object.

Usage

cgarchfit(spec, data, spd.control = list(lower = 0.1, upper = 0.9, type = "pwm", 
kernel = "epanech"), fit.control = list(eval.se = TRUE, stationarity = TRUE, 
scale = FALSE), solver = "solnp", solver.control = list(), out.sample = 0, 
cluster = NULL, fit = NULL, VAR.fit = NULL, realizedVol = NULL,...) 

Arguments

Details

The Copula-GARCH models implemented can either be time-varying of DCC variety else static. The multivariate Normal and Student distributions are used in the construction of the copulas, and 3 transformation methods are available (parametric, semi-parametric, and empirical). For the semi-parametric case the ‘spd’ package of the author is available to download from CRAN and fits a Gaussian kernel in the interior and gpd distribution for the tails (see that package for more details).
The static copula allows for the estimation of the correlation matrix either by Maximum Likelihood or the Kendall method for the multivariate Student.
Note that the ‘cgarchfit’ method will assign to the global environment the uGARCHmultifit once that is estimated in order to allow the routine to be restarted should something go wrong (it should show up as ‘.fitlist’).

Value

A cGARCHfit Object containing details of the Copula-GARCH fit.

Note

There is no check on the VAR.fit list passed to the method so particular care should be exercised so that the same data used in the fitting routine is also used in the VAR fit routine. This must have been called with the option postpad ‘constant’. The ability to pass this list of the pre-calculated VAR model is particularly useful when comparing different models (such as DCC GARCH, GO GARCH etc) using the same dataset and VAR method (i.e. the same first stage conditional mean filtration). Though the classical VAR estimation is very fast and may not require this extra step, the robust method is slow and therefore benefits from calculating this only once.
For extensive examples look in the ‘rmgarch.tests’ folder.

Author(s)

Alexios Galanos

function: Copula-GARCH Simulation

Description

Method for creating a Copula-GARCH simulation object.

Usage

cgarchsim(fit, n.sim = 1000, n.start = 0, m.sim = 1, 
startMethod = c("unconditional", "sample"), presigma = NULL, preresiduals = NULL, 
prereturns = NULL, preR = NULL, preQ = NULL, preZ = NULL, rseed = NULL, 
mexsimdata = NULL, vexsimdata = NULL, cluster = NULL, only.density = FALSE, 
prerealized = NULL, ...)

Arguments

Details

Since there is no explicit forecasting routine, the user should use this method for incrementally building up n-ahead forecasts by simulating 1-ahead, obtaining the means of the returns, sigma, Rho etc and feeding them to the next round of simulation as starting values. The ‘rmgarch.tests’ folder contains specific examples which illustrate this particular point.

Value

A cGARCHsim object containing details of the Copula-GARCH simulation.

Author(s)

Alexios Galanos

References

Joe, H. Multivariate Models and Dependence Concepts, 1997, Chapman \& Hall, London.
Genest, C., Ghoudi, K. and Rivest, L. A semiparametric estimation procedure of dependence parameters in multivariate families of distributions, 1995, Biometrika, 82, 543-552.

function: Copula-GARCH Specification

Description

Method for creating a Copula-GARCH specification object prior to fitting.

Usage

cgarchspec(uspec, VAR = FALSE, robust = FALSE, lag = 1, lag.max = NULL, 
lag.criterion = c("AIC", "HQ", "SC", "FPE"), external.regressors = NULL, 
robust.control = list(gamma = 0.25, delta = 0.01, nc = 10, ns = 500), 
dccOrder = c(1, 1), asymmetric = FALSE, 
distribution.model = list(copula = c("mvnorm", "mvt"), 
method = c("Kendall", "ML"), time.varying = FALSE, 
transformation = c("parametric", "empirical", "spd")), 
start.pars = list(), fixed.pars = list()) 

Arguments

Details

The transformation method allows for parametric (Inference-Functions for Margins), empirical (Pseudo-Likelihood) and semi-parametric (via the spd package).
When the Student Copula is jointly estimated with student margins having so that a common shape parameter is obtained, this results in the multivariate Student distribution. When estimating the Student Copula with disparate margins, a meta-student distribution is obtained. Additionally, the correlation parameter in the static Student Copula may be estimated either by Kendall's tau transformation or Maximum Likelihood.
The robust option allows for a robust version of VAR based on the multivariate Least Trimmed Squares Estimator described in Croux and Joossens (2008).

Value

A cGARCHspec object containing details of the Copula-GARCH specification.

Author(s)

Alexios Galanos

A Correlation Distance Measure

Description

Given an array of correlation snapshots in time, returns a matrix of some rolling distance measure on the correlations.

Usage

cordist(R, distance = c("ma","ms","meda","meds","eigen", "cmd"), n = 25, 
plot = TRUE, dates = NULL, title = NULL)

Arguments

Details

This function provides for a visualization of dynamic correlation distance between periods with a number of plausible measures including “ma” (mean absolute), “ms” (mean squared), “meda” (median absolute), “meds” (median squared) “eigen” (largest eigenvalue difference) and “cmd” (correlation matrix distance). See the references for more details.

Value

A symmetric matrix of the rolling distance measure for each period.

Author(s)

Alexios Galanos

References

Munnix, M. C., Shimada, T., Schafer, R., Leyvraz, F., Seligman, T. H., Guhr, T., & Stanley, H. E. (2012). Identifying states of a financial market. Scientific Reports 2.
Herdin, M., Czink, N., Ozcelik, H., & Bonek, E. (2005). Correlation matrix distance, a meaningful measure for evaluation of non-stationary MIMO channels. Vehicular Technology Conference, 2005, IEEE 61st, 1, 136–140.

function: DCC-GARCH Filter

Description

Method for creating a DCC-GARCH filter object.

Usage

dccfilter(spec, data, out.sample = 0, filter.control = list(n.old = NULL), 
cluster = NULL, varcoef = NULL, realizedVol = NULL, ...) 

Arguments

Value

A DCCfilter object containing details of the DCC-GARCH filter.

Note

The ‘n.old’ option in the filter.control argument is key in replicating conditions of the original fit. That is, if you want to filter a dataset consisting of an expanded dataset (versus the original used in fitting), but want to use the same assumptions as the original dataset then the ‘n.old’ argument denoting the original number of data points passed to the dccfit function must be provided. This is then used to ensure that some calculations which make use of the full dataset (unconditional starting values for the garch filtering and the dcc model) only use the first ‘n.old’ points thus replicating the original conditions making filtering appropriate for rolling 1-ahead forecasting.
For extensive examples look in the ‘rmgarch.tests’ folder.

Author(s)

Alexios Galanos

function: DCC-GARCH Fit

Description

Method for creating a DCC-GARCH fit object.

Usage

dccfit(spec, data, out.sample = 0, solver = "solnp", solver.control = list(), 
fit.control = list(eval.se = TRUE, stationarity = TRUE, scale = FALSE), 
cluster = NULL, fit = NULL, VAR.fit = NULL, realizedVol = NULL, ...)

Arguments

Details

The 2-step DCC estimation fits a GARCH-Normal model to the univariate data and then proceeds to estimate the second step based on the chosen multivariate distribution. Because of this 2-step approach, standard errors are expensive to calculate and therefore the use of parallel functionality, built into both the fitting and standard error calculation routines is key. The switch to turn off the calculation of standard errors through the ‘fit.control’ option could be quite useful in rolling estimation such as in the dccroll routine.
The optional ‘fit’ argument allows to pass your own uGARCHmultifit object instead of having the routine estimate it. This is very useful in cases of multiple use of the same fit and problems in convergence which might require a more hands on approach to the univariate fitting stage. However, it is up to the user to ensure consistency between the ‘fit’ and supplied ‘spec’.

Value

A DCCfit object containing details of the DCC-GARCH fit.

Note

There is no check on the VAR.fit list passed to the method so particular care should be exercised so that the same data used in the fitting routine is also used in the VAR fit routine. This this must have been called with the option postpad ‘constant’. The ability to pass this list of the pre-calculated VAR model is particularly useful when comparing different models (such as copula-GARCH, GO-GARCH etc) using the same dataset and VAR method (i.e. the same first stage conditional mean filtration). Though the classical VAR estimation is very fast and may not require this extra step, the robust method is slow and therefore benefits from calculating this only once.
For extensive examples look in the ‘rmgarch.tests’ folder.

Author(s)

Alexios Galanos

function: DCC-GARCH Forecast

Description

Method for creating a DCC-GARCH forecast object.

Usage

dccforecast(fit, n.ahead = 1, n.roll = 0, 
external.forecasts = list(mregfor = NULL, vregfor = NULL), cluster = NULL, ...) 

Arguments

Details

When using n.roll, it is assumed that dccfit was called with argument ‘out.sample’ being large enough to cover n-rolling forecasts.
When n.roll = 0, all forecasts are based on an unconditional n-ahead forecast routine based on the approximation method described in ENGLE and SHEPPARD (2001) paper (see reference below). If any external regressors are present, then the user must pass in their unconditional forecasts in the ‘external.forecasts’ list, as matrices with dimensions equal to n.ahead x n.assets. This assumes that the univariate GARCH specifications share common external regressors (this may change in the future).
When n.roll>0 and n.ahead = 1, then this is a pure rolling forecast based on the available out.sample data provided for in the call to the fit routine. It is also assumed that if any external regressors were passed to the fit routine that they contained enough values to cover the out.sample period so that they could be used in this forecast scenario.
The case of n.roll > 0 AND n.ahead > 1 is not implemented.

Value

A DCCforecast object containing details of the DCC-GARCH forecast.

Author(s)

Alexios Galanos

References

Engle, R.F. and Sheppard, K. 2001, Theoretical and empirical properties of dynamic conditional correlation multivariate GARCH, NBER Working Paper.

function: DCC-GARCH Rolling Forecast

Description

Method for creating a DCC-GARCH rolling forecast object.

Usage

dccroll(spec, data, n.ahead = 1, forecast.length = 50, refit.every = 25, 
n.start = NULL, refit.window = c("recursive", "moving"), window.size = NULL, 
solver = "solnp", solver.control = list(), 
fit.control = list(eval.se = TRUE, stationarity = TRUE, scale = FALSE), 
cluster = NULL, save.fit = FALSE, save.wdir = NULL, realizedVol = NULL, 
clusterOnAssets=FALSE, ...)

Arguments

Value

A DCCroll object containing details of the DCC-GARCH rolling forecast.

Author(s)

Alexios Galanos

function: DCC-GARCH Simulation

Description

Method for creating a DCC-GARCH simulation object.

Usage

dccsim(fitORspec, n.sim = 1000, n.start = 0, m.sim = 1, 
startMethod = c("unconditional", "sample"), presigma = NULL, preresiduals = NULL, 
prereturns = NULL, preQ = NULL, preZ = NULL, Qbar = NULL, Nbar = NULL, 
rseed = NULL, mexsimdata = NULL, vexsimdata = NULL, cluster = NULL, 
VAR.fit = NULL, prerealized = NULL, ...)

Arguments

Details

In order to pass a correct specification to the filter routine, you must ensure that it contains the appropriate ‘fixed.pars’ in both the multivariate DCC part of the specification as well as the multiple univariate specification part, for which the method setfixed<- should be used.

Value

A DCCsim object containing details of the DCC-GARCH simulation.

Author(s)

Alexios Galanos

function: DCC-GARCH Specification

Description

Method for creating a DCC-GARCH specification object prior to fitting.

Usage

dccspec(uspec, VAR = FALSE, robust = FALSE, lag = 1, lag.max = NULL, 
lag.criterion = c("AIC", "HQ", "SC", "FPE"), external.regressors = NULL, 
robust.control = list("gamma" = 0.25, "delta" = 0.01, "nc" = 10, "ns" = 500), 
dccOrder = c(1,1), model = c("DCC", "aDCC", "FDCC"), groups = rep(1, length(uspec@spec)), 
distribution = c("mvnorm", "mvt", "mvlaplace"), start.pars = list(), fixed.pars = list()) 

Arguments

Details

The robust option allows for a robust version of VAR based on the multivariate Least Trimmed Squares Estimator described in Croux and Joossens (2008).

Value

A DCCspec object containing details of the DCC-GARCH specification.

Note

The FDCC model of Billio, Caporin and Gobbo (2006) allows different DCC parameters to govern the dynamics of the correlation of distinct groups. The drawback is a somewhat larger parameter set, and no correlation targeting. Still, it remains a feasible model for not too large a number of groups, and avoids the unrealistic assumption, particularly for large datasets, of one parameter governing all the dynamics, as in the DCC model. Note that the group indices must be increasing (unless all 1), which means that you should arrange your dataset so that the assets are ordered by their groups.

Author(s)

Alexios Galanos

References

Billio, M., Caporin, M., & Gobbo, M. 2006, Flexible dynamic conditional correlation multivariate GARCH models for asset allocation, Applied Financial Economics Letters, 2(02), 123–130.
Croux, C. and Joossens, K. 2008, Robust estimation of the vector autoregressive model by a least trimmed squares procedure, COMPSTAT, 489–501.
Cappiello, L., Engle, R.F. and Sheppard, K. 2006, Asymmetric dynamics in the correlations of global equity and bond returns, Journal of Financial Econometrics 4, 537–572.
Engle, R.F. and Sheppard, K. 2001, Theoretical and empirical properties of dynamic conditional correlation multivariate GARCH, NBER Working Paper.

data: Dow Jones 30 Constituents Closing Value log Weekly Return

Description

Dow Jones 30 Constituents closing value weekly (Friday) log returns from 1987-03-16 to 2009-02-03 from Yahoo Finance. Note that AIG was replaced by KFT (Kraft Foods) on September 22, 2008. This is not reflected in this data set as that would bring the starting date of the data to 2001. When data was not available for a Friday, the closest previous close for which data was available was used.

Usage

data(dji30retw)

Format

A data.frame containing 30x1141 observations.

Source

Yahoo Finance

Class "fMoments"

Description

Object returned from calling fmoments.

Objects from the Class

Objects can be created by calls of the form new("fMoments", ...).

Slots

moments:

Object of class "vector" A list with the (roll+1) n-ahead forecast moment matrices.

model:

Object of class "vector" A list with details of data generating process.

Methods

show

signature(object = "fMoments"): Summary method.

fitted

signature(object = "fMoments"): Conditional mean forecast matrix.

rcov

signature(object = "fMoments"): Conditional covariance forecast array.

rcoskew

signature(object = "fMoments"): Conditional third co-moment array.

rcokurt

signature(object = "fMoments"): Conditional fourth co-moment array.

Author(s)

Alexios Galanos

Examples

showClass("fMoments")

Class "fScenario"

Description

Object returned from calling fscenario.

Objects from the Class

Objects can be created by calls of the form new("fScenario", ...).

Slots

scenario:

Object of class "vector" A list with the (roll+1) scenario matrices.

model:

Object of class "vector" A list with details of data generating process.

Methods

show

signature(object = "fScenario"): Summary method.

goget

signature(object = "fScenario"): Get a specified ‘arg’ from the object (only ‘scenario’ used).

fitted

signature(object = "fScenario"): Returns an array of the simulated scenario returns, of dimensions n.sim by n.assets by (roll+1), with third dimension labels the actual forecast time index, and second dimension labels the asset names. The last forecast scenario will always be completely out of sample so the time index label for that is generated using the generatefwd function in the rugarch package.

Author(s)

Alexios Galanos

Fast Fixed Point ICA

Description

The fast fixed point algorithm for independent component analysis and projection pursuit based on the direct translation to R of the FastICA program of the original authors at the Helsinki University of Technology.

Usage

fastica(X, approach = c("symmetric", "deflation"), n.comp = dim(X)[2], demean = TRUE, 
pca.cov = c("ML", "LW", "ROB", "EWMA"), gfun = c("pow3", "tanh", "gauss", "skew"), 
finetune = c("none", "pow3", "tanh", "gauss", "skew"), tanh.par = 1, gauss.par = 1, 
step.size = 1, stabilization = FALSE, epsilon = 1e-4, maxiter1 = 1000, maxiter2 = 5, 
A.init = NULL, pct.sample = 1, firstEig = NULL, lastEig = NULL, 
pcaE = NULL, pcaD = NULL, whiteSig = NULL, whiteMat = NULL, dewhiteMat = NULL, 
rseed = NULL, trace = FALSE, ...)

Arguments

Details

The fastica program is a direct translation into R of the FastICA Matlab program of Gaevert, Hurri, Saerelae, and Hyvaerinen with some extra features. All computations are currently implemented in R so for very large dimensional sets alternative implementations may be faster. Porting part of the code to C++ may be implemented in a future version.

Value

A list containing the following values:

Note

Since version 1.0-3 the multidimensional signal matrix is now the usual row by column matrix, where the rows represent observations and columns the signals. Before this version, the reverse was true in keeping with the original version of the program.
Dimensionality reduction can be achieved in the PCA stage by use of either n.comp in which case the n.comp largest eigenvalues are chosen, else by selection of firstEig and lastEig which overwrites the choice of n.comp.

Author(s)

Hugo Gaevert, Jarmo Hurri, Jaakko Saerelae, and Aapo Hyvaerinen for the original FastICA package for matlab.
Alexios Galanos for this R-port.

References

Hyvaerinen, A. and Oja,.E , 1997, A fast fixed-point algorithm for independent component analysis, Neural Computation, 9(7), 1483-1492. Reprinted in Unsupervised Learning, G. Hinton and T. J. Sejnowski, 1999, MIT Press.

Examples

## Not run: 
# create a set of independent signals S, glued together by a mixing matrix A
# (note the notation and matrix multiplication direction as we are dealing with
# row rather than column vectors)
set.seed(100)
S <- matrix(runif(10000), 5000, 2)
A <- matrix(c(1, 1, -1, 2), 2, 2, byrow = TRUE)
# the mixed signal X
X = S %*% t(A)
# The function centers and whitens (by the eigenvalue decomposition of the 
# unconditional covariance matrix)  the data before applying the theICA algorithm.
IC <- fastica(X, n.comp = 2, approach = "symmetric", gfun = "tanh", trace  = TRUE, 
A.init = diag(2))

# demeaned data:
X_bar = scale(X, scale = FALSE)

# whitened data:
X_white = X_bar %*% t(IC$whiteningMatrix)

# check whitening:
# check correlations are zero
cor(X_white)
# check diagonals are 1 in covariance
cov(X_white)

# check that the estimated signals(S) multiplied by the
# estimated mxing matrix (A) are the same as the original dataset (X)
round(head(IC$S %*% t(IC$A)), 12) == round(head(X), 12)

# do some plots:
par(mfrow = c(1, 3))
plot(IC$S %*% t(IC$A), main = "Pre-processed data")
plot(X_white, main = "Whitened and Centered components")
plot(IC$S, main = "ICA components")

## End(Not run)

Moment Based Forecast Generation

Description

Generates n-ahead forecast moment matrices given a choice of data generating processes.

Usage

fmoments(spec, Data, n.ahead = 1, roll  = 0, solver = "solnp", 
solver.control = list(), fit.control = list(eval.se = FALSE), 
cluster = NULL, save.output = FALSE, save.dir = getwd(), 
save.name = paste("M", sample(1:1000, 1), sep = ""), ...)

Arguments

Details

The function allows to generate forecast covariance matrices for use in the QP based EV model, and also for the “gogarch” model higher co-moment matrices for use in the Utility maximization model implemented separately.

Value

A fMoments object containing the forecast moments (list of length roll+1) and the model details (list).

Author(s)

Alexios Galanos

Scenario Generation

Description

Generates a 1-ahead forecast scenario given a choice of data generating processes (for use in stochastic programming or risk management).

Usage

fscenario(Data, sim = 1000, roll = 0, 
	model = c("gogarch", "dcc", "cgarch", "var", "mdist"), 
	spec = NULL, 
	var.model = list(lag = 1, lag.max = NULL, 
				lag.criterion = c("AIC", "HQ", "SC", "FPE"), 
				robust = FALSE, robust.control = list("gamma" = 0.25, 
				"delta" = 0.01, "nc" = 10, "ns" = 500)),
	mdist.model = list(distribution = c("mvn", "mvt", "manig"), 
				AR = TRUE, lag = 1),
	spd.control = list(lower = 0.1, upper = 0.9, type = "pwm", 
				kernel = "epanech"),
	cov.method = c("ML", "LW", "EWMA", "MVE", "MCD", "MVT", "BS"),
	cov.options = list(shrinkage=-1, lambda = 0.96),
	solver = "solnp", solver.control = list(), 
	fit.control = list(eval.se = FALSE), 
	cluster = NULL, save.output = FALSE, save.dir = getwd(),
	save.name = paste("S", sample(1:1000, 1), sep = ""), rseed  = NULL, ...)

Arguments

Details

The functionality here provides some wrapper functions, to create 1-ahead (and optionally rolling, useful for backtesting) scenarios for use in portfolio optimization using stochastic programming methods. The nature of these data generating processes (as implemented here) and resulting optimization problems results in the so called anticipative class of stochastic programming models. If save.output is chosen, and given a save.dir, the scenario is saved (using save.name) and an object is returned containing an empty list for the scenario but with a model details list and the seed values. This can then be passed on to the goload function which can read from the directory and return a complete object with the scenario.

Value

A fScenario object containing the scenario and the model details (list). The scenario list contains a list of the (roll+1) simulated forecast scenarios, the list of (roll+1) simulated forecast residuals, the forecast conditional mean, the forecast covariance and the list of random generator seed values used for replication. In addition, for the gogarch model the ICA whitening (K) and rotation matrices are also returned and required for replication of results (these may be entered in the ‘gogarchspec’ function). Use the fitted method on the object to extract the simulated returns forecast.

Author(s)

Alexios Galanos

Class: GO-GARCH portfolio density

Description

Class for the GO-GARCH portfolio density

Objects from the Class

The class is returned by calling the function convolution on objects of class goGARCHfit, goGARCHfilter, goGARCHforecast, goGARCHsim and goGARCHroll

Slots

dist:

A list with the portfolio density and other details.

model:

A list with the model details carried across objects.

Methods

dfft

signature(object = "goGARCHfft"): The takes additional argument “index” to indicate the particular time point, and returns an interpolated density function which may be called like any other “d” type density function.

pfft

signature(object = "goGARCHfft") The takes additional argument “index” to indicate the particular time point, and returns an interpolated distribution function which may be called like any other “p” type distribution function.

qfft

signature(object = "goGARCHfft") This takes additional argument “index” to indicate the particular time point, and returns an interpolated quantile function which may be called like any other “q” type quantile function. This may also be used to generate pseudo-random variables from the distribution by using random standard uniform numbers as inputs.

nportmoments

signature(object = "goGARCHfft"): Calculate and returns a matrix of the first 4 standardized moments by evaluation of the portfolio density using quadrature based method (i.e. calling R's “integrate” function on the portfolio FFT based density). Depending on the GOGARCH class the density was based (e.g. goGARCHfit vs goGARCHforecast), the format of the output will be different, and generally follow the format ‘rules’ of that class.

notes

In the case that convolution was called on a goGARCHforecast or goGARCHroll object, the dist slot will contain the max of n.ahead or n.roll. There should be no confusion here since the multivariate forecast methods in rmgarch only allow either n.ahead>1 with n.roll = 0 (pure unconditional), or n.ahead = 1 with n.roll>=0 (pure rolling), and only the latter in the case of a gogarchroll. While the nportmoments method reconstitutes the forecasts into a more familiar form (n.ahead x n.moments x (n.roll+1)), this does not make sense for the distribution methods (d*, p*, and q*), and it is understood that when the user calls for example dfft(object, index=5) on an object created from a forecast with n.ahead=10 and n.roll=0, the index is meant to indicate the unconditional density forecast at time T+5. Similarly, when calling codedfft(object, index=0) on an object created from a forecast with n.ahead=1 and n.roll = 1 (remember that n.roll is zero based), the index is meant to indicate the first (of two, since rolls = 0:1) rolling forecast density.

Author(s)

Alexios Galanos

class: GO-GARCH Filter Class

Description

Class for the GO-GARCH filtered object.

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.

model:

Object of class "vector" containing details of the GOGARCH model specification.

Extends

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

Methods

as.matrix

signature(x = "goGARCHfilter"):
function:
as.matrix(x, which = "A")
This returns four types of matrices relating to the estimation of the independent components in the GO-GARCH model. Valid choices are “A” for the mixing matrix, “W” for the unmixing matrix, “U” for the rotational matrix and “K” for the whitening matrix, “Kinv” for the de-whitening matrix.

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. For a dimensionality reduced system, this is NA.

coef

signature(object = "goGARCHfilter"): Extraction of independent factor GARCH model coefficients.

fitted

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

residuals

signature(object = "goGARCHfilter"): Extracts the conditional mean equation residuals.

convolution

signature(object = "goGARCHfilter"):
function:
convolution(object, weights, fft.step = 0.001, fft.by = 0.0001, fft.support = c(-1, 1), support.method = c("user", "adaptive"), use.ff = TRUE, cluster = NULL, trace = 0,...)
The convolution method takes a goGARCHfit 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 via the use of a cluster object as elsewhere in this package.

nisurface

signature(object = "goGARCHfilter"):
function:
nisurface(object, type = "cov", pair = c(1, 2), factor = c(1,2), plot = TRUE)
Creates the covariance or correlation (determined by “type” being either “cov” or “cor”) news impact surface for a pair of assets and factors. Since the shocks impact the factors independently, the news impact surface is a combination of the independent news impact curves of the factors which when combined via the mixing matrix A, create the dynamics for the underlying asset-factor surface function

portmoments

signature(object = "goGARCHfilter"):
function:
gportmoments(object, weights)
Calculates the first 4 portfolio moments using the geometric properties of the model, given a vector or matrix of asset weights. If a matrix is given it must have row dimension equal to the row dimension of the filtered dataset (i.e. less any lags), else if a vector is given it will be replicated for all time points.

rcoskew

signature(object = "goGARCHfilter") function:
rcoskew(object, standardize = TRUE, from = 1, to = 1)
Returns the 'time-varying' NxN^2 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 per call.

rcokurt

signature(object = "goGARCHfilter") function:
rcokurt(object, standardize = TRUE, from = 1, to = 1)
Returns the 'time-varying' NxN^3 cokurtosis 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 models with less than 100 assets.

rcov

signature(object = "goGARCHfilter"): Returns the time-varying NxN covariance matrix in array format. A further argument ‘output’ allows to switch between “array” and “matrix” returned object.

rcor

signature(object = "goGARCHfilter"): Returns the time-varying NxN correlation matrix in array format. A further argument ‘output’ allows to switch between “array” and “matrix” returned object.

betacovar

signature(object = "goGARCHfilter"): function:
betacovar(object, weights, asset = 1, cluster = NULL)
Returns the covariance beta given a matrix (of length equal to the number of rows of the original data, or vector which is then recycled to the number of rows of the original data) of benchmark weights and the asset number.

betacoskew

signature(object = "goGARCHfilter"): function:
betacoskew(object, weights, asset = 1, cluster = NULL)
Returns the coskewness beta given a matrix (of length equal to the number of rows of the original data, or vector which is then recycled to the number of rows of the original data) of benchmark weights and the asset number.

betacokurt

signature(object = "goGARCHfilter"): function:
betacokurt(object, weights, asset = 1, cluster = NULL)
Returns the cokurtosis beta given a matrix (of length equal to the number of rows of the original data, or vector which is then recycled to the number of rows of the original data) of benchmark weights and the asset number.

show

signature(object = "goGARCHfilter"): Summary method.

Note

The reference by Paolella (2007) contains more details on the algorithm for the characteristic function inversion via FFT. The application of this method in a related model can be found in Chen (2007). The de Athayde and Flores (2002) paper is the basis for the geometric properties of the higher moment tensors in finance.

Author(s)

Alexios Galanos

References

de Athayde, G.M. and Flores Jr, R.G. 2002, On Certain Geometric Aspects of Portfolio Optimisation with Higher Moments, mimeo.
Broda, S.A. and Paolella, M.S. 2009, CHICAGO: A Fast and Accurate Method for Portfolio Risk Calculation, Journal of Financial Econometrics 7(4), 412–436 .
Paolella, M.S. 2007, Intermediate Probability - A Computational Approach, Wiley-Interscience.
Schmidt, R., Hrycej, T. and Stutzle 2006, Multivariate distribution models with generalized hyperbolic margins, Computational Statistics \& Data Analysis 50(8), 2065-2096.

class: GO-GARCH Fit Class

Description

Class for the GO-GARCH fitted object.

Objects from the Class

The class is returned by calling the function gogarchfit.

Slots

mfit:

Multivariate fit object.

model:

Object of class "vector" containing details of the GO-GARCH model specification.

Extends

Class "mGARCHfit", directly. Class "GARCHfit", by class "mGARCHfit", distance 2. Class "rGARCH", by class "mGARCHfit", distance 3.

Methods

as.matrix

signature(x = "goGARCHfit"): function:
as.matrix(x, which = "A")
This returns four types of matrices relating to the estimation of the independent components in the GO-GARCH model. Valid choices are “A” for the mixing matrix, “W” for the unmixing matrix, “U” for the rotational matrix and “K” for the whitening matrix, “Kinv” for the de-whitening matrix.

coef

signature(object = "goGARCHfit"): extraction of independent factor GARCH model coefficients.

convolution

signature(object = "goGARCHfit"):
function:
convolution(object, weights, fft.step = 0.001, fft.by = 0.0001, fft.support = c(-1, 1), support.method = c("user", "adaptive"), use.ff = TRUE, cluster = NULL, trace = 0,...)
The convolution method takes a goGARCHfit 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 via the use of a cluster object as elsewhere in this package.

fitted

signature(object = "goGARCHfit"): Extracts the conditional mean equation fitted values.

residuals

signature(object = "goGARCHfit"): Extracts the conditional mean equation residuals.

likelihood

signature(object = "goGARCHfit"): 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. For a dimensionality reduced system, this is NA.

nisurface

signature(object = "goGARCHfit"):
function:
nisurface(object, type = "cov", pair = c(1, 2), factor = c(1,2), plot = TRUE)
Creates the covariance or correlation (determined by “type” being either “cov” or “cor”) news impact surface for a pair of assets and factors. Since the shocks impact the factors independently, the news impact surface is a combination of the independent news impact curves of the factors which when combined via the mixing matrix A, create the dynamics for the underlying asset-factor surface function.

gportmoments

signature(object = "goGARCHfit"):
function:
gportmoments(object, weights)
Calculates the first 4 portfolio moments using the geometric properties of the model, given a vector or matrix of asset weights. If a matrix is given it must have row dimension equal to the row dimension of the filtered dataset (i.e. less any lags), else if a vector is given it will be replicated for all time points.

rcoskew

signature(object = "goGARCHfit") function:
rcoskew(object, standardize = TRUE, from = 1, to = 1)
Returns the 'time-varying' NxN^2 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 per call.

rcokurt

signature(object = "goGARCHfit") function:
rcokurt(object, standardize = TRUE, from = 1, to = 1)
Returns the 'time-varying' NxN^3 cokurtosis 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 models with less than 100 assets.

rcov

signature(object = "goGARCHfit"): Returns the time-varying NxN covariance matrix in array format unless ‘output’ is set to “matrix” in which case the array is flattened and the lower and main diagonal time varying values are returned (and if a date exists, then the returned object is of class xts).

rcor

signature(object = "goGARCHfit"): Returns the time-varying NxN correlation matrix in array format unless ‘output’ is set to “matrix” in which case the array is flattened and the lower and main diagonal time varying values are returned (and if a date exists, then the returned object is of class xts).

betacovar

signature(object = "goGARCHfit"): function:
betacovar(object, weights, asset = 1, cluster = NULL)
Returns the covariance beta given a matrix (of length equal to the number of rows of the original data, or vector which is then recycled to the number of rows of the original data) of benchmark weights and the asset number.

betacoskew

signature(object = "goGARCHfit"): function:
betacoskew(object, weights, asset = 1, cluster = NULL)
Returns the coskewness beta given a matrix (of length equal to the number of rows of the original data, or vector which is then recycled to the number of rows of the original data) of benchmark weights and the asset number.

betacokurt

signature(object = "goGARCHfit"): function:
betacokurt(object, weights, asset = 1, cluster = NULL)
Returns the cokurtosis beta given a matrix (of length equal to the number of rows of the original data, or vector which is then recycled to the number of rows of the original data) of benchmark weights and the asset number.

show

signature(object = "goGARCHfit"): Summary method.

Note

The reference by Paolella (2007) contains more details on the algorithm for the characteristic function inversion via FFT. The application of this method in a related model can be found in Chen (2007). The de Athayde and Flores (2002) paper is the basis for the geometric properties of the higher moment tensors in finance.

Author(s)

Alexios Galanos

References

de Athayde, G.M. and Flores Jr, R.G. 2002, On Certain Geometric Aspects of Portfolio Optimisation with Higher Moments, mimeo.
Broda, S.A. and Paolella, M.S. 2009, CHICAGO: A Fast and Accurate Method for Portfolio Risk Calculation, Journal of Financial Econometrics 7(4), 412–436 .
Paolella, M.S. 2007, Intermediate Probability - A Computational Approach, Wiley-Interscience.
Schmidt, R., Hrycej, T. and Stutzle 2006, Multivariate distribution models with generalized hyperbolic margins, Computational Statistics \& Data Analysis 50(8), 2065-2096.

Examples

## Not run: 
data(dji30ret)
spec = gogarchspec(mean.model = list(demean = "constant"),
variance.model = list(model = "sGARCH", garchOrder = c(1,1), submodel = NULL),
distribution.model = list(distribution = "manig"), ica = "fastica")
fit = gogarchfit(spec = spec, data  = dji30ret[,1:4, drop = FALSE],
out.sample = 50, gfun = "tanh")
# The likelihood of the model
likelihood(fit)
# the GARCH coefficients of the independent factors
coef(fit)
# a news-impact surface plot
#ni = nisurface(fit, type = "cov", pair = c(1, 2), factor = c(1,2), plot = TRUE)
# the time varying correlation array
mc = rcor(fit)
# plot(mc[1,2,], type = "l")
# The moments of an equally weighted portfolio (subtract the out.sample from dimension)
gm = gportmoments(fit, weights = matrix(1/4, ncol = 4,
nrow = dim(dji30ret)[1]-50), debug = TRUE)

## End(Not run)

class: GO-GARCH Forecast Class

Description

Class for the GO-GARCH forecast.

Objects from the Class

The class is returned by calling the function gogarchforecast.

Slots

mforecast:

Multivariate forecast object.

model:

Object of class "vector" containing details of the GOGARCH model specification.

Extends

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

Methods

convolution

signature(object = "goGARCHforecast"):
function:
convolution(object, weights, fft.step = 0.001, fft.by = 0.0001, fft.support = c(-1, 1), support.method = c("user", "adaptive"), use.ff = TRUE, cluster = NULL, 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 total forecast horizon. 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. The option for parallel computation is available via the use of a cluster object as elsewhere in this package. There is no special treatment of the forecast type here (unconditional or rolling), since either n.ahead with no roll or rolling with 1-ahead only choices are available for the gogarchforecast method. This means that the stored object does not distringuish between an unconditional or rolling forecast, calculating the density for all points (see note).

gportmoments

signature(object = "goGARCHforecast"):
function:
gportmoments(object, weights)
Calculates the first 4 standardized portfolio moments using the geometric properties of the model, given a matrix of asset weights with row dimension equal to the forecast n.ahead or n.roll horizon. Returns an array of dimensions n.ahead x 4 (moments) x n.roll, with the third array dimension labelled with the T+0 index times. If the number of assets > 100, then the kurtosis is not returned (see cokurtosis restrictions below).

rcoskew

signature(object = "goGARCHforecast"):
function:
rcoskew(object, standardize = TRUE, from = 1, to = 1, roll = 0)
Returns the 'time-varying' NxN^2 (coskewness tensor) x (to:from|roll) in array format. The “from” and “to” options indicate the time indices for which to return the array and “roll” the rolling index (base=0). The third dimension array label denotes the T+i (i=from:to) forecast horizon given the T+0 roll index which is returned as an attribute (attr(,“T+0”)) of the array. The “standardize” option indicates whether the coskewness should be standardized by the conditional sigma (see equations in vignette). It is also possible to set roll to the character ‘all’ in which case all the rolling 1-ahead forecasts are returned in an n by n^2 by (n.roll+1) array with 3rd dimension label the T+0 dates (instead of being an attribute).

rcokurt

signature(object = "goGARCHforecast"):
function:
rcokurt(object, standardize = TRUE, from = 1, to = 1, roll = 0)
Returns the 'time-varying' NxN^3 (cokurtosis tensor) x (to:from|roll) in array format. The “from” and “to” options indicate the time indices for which to return the array and “roll” the rolling index (base=0). Because of memory issues, this is only returned when the number of assets are less than 100. The third dimension array label denotes the T+i (i=from:to) forecast horizon given the T+0 roll index which is returned as an attribute (attr(,“T+0”)) of the array. The “standardize” option indicates whether the cokurtosis should be standardized by the conditional sigma (see equations in vignette). It is also possible to set roll to the character ‘all’ in which case all the rolling 1-ahead forecasts are returned in an n by n^3 by (n.roll+1) array with 3rd dimension label the T+0 dates (instead of being an attribute.

rcov

signature(object = "goGARCHforecast"): Returns the conditional covariances, in a list of length (n.roll+1), with names the T+0 index, and each list slot having an array of dimensions n.asset x n.asset x n.ahead, with the third array dimension labelled as T+i (i>0). A further argument ‘output’ allows to switch between “array” and “matrix” returned object.

rcor

signature(object = "goGARCHforecast"): Returns the conditional correlations, in a list of length (n.roll+1), with names the T+0 index, and each list slot having an array of dimensions n.asset x n.asset x n.ahead, with the third array dimension labelled as T+i (i>0). A further argument ‘output’ allows to switch between “array” and “matrix” returned object.

coef

signature(object = "goGARCHforecast"): Extraction of independent factor GARCH model coefficients saved from the goGARCHfit object.

fitted

signature(object = "goGARCHforecast"): Extracts the conditional mean forecast values. Returns an n.ahead x n.assets x (n.roll+1) array where the third dimension array labels are the T+0 index times.

sigma

signature(object = "goGARCHforecast"): Extracts the conditional sigma forecast values. Returns an n.ahead x n.assets x (n.roll+1) array where the third dimension array labels are the T+0 index times. Takes optional argument “factors” (default TRUE) denoting whether to return the factor conditional sigma or the transformed sigma for the assets.

as.matrix

signature(x = "goGARCHforecast"):
function:
as.matrix(x, which = "A")
This returns four types of matrices relating to the estimation of the independent components in the GO-GARCH model. Valid choices are “A” for the mixing matrix, “W” for the unmixing matrix, “U” for the rotational matrix and “K” for the whitening matrix, “Kinv” for the de-whitening matrix.

betacovar

signature(object = "goGARCHforecast"): function:
betacovar(object, weights, asset = 1)
Returns the covariance beta given a matrix (of length equal to the number of rows of the forecast horizon, or vector which is then recycled to the number of rows of the forecast horizon) of benchmark weights and the asset number.

betacoskew

signature(object = "goGARCHforecast"): function:
betacoskew(object, weights, asset = 1)
Returns the coskewness beta given a matrix (of length equal to the number of rows of the forecast horizon, or vector which is then recycled to the number of rows of the forecast horizon) of benchmark weights and the asset number.

betacokurt

signature(object = "goGARCHforecast"): function:
betacokurt(object, weights, asset = 1)
Returns the cokurtosis beta given a matrix (of length equal to the number of rows of the forecast horizon, or vector which is then recycled to the number of rows of the forecast horizon) of benchmark weights and the asset number.

show

signature(object = "goGARCHforecast"): Summary method.

Note

The reference by Chen et al (2010) and 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 some of the geometric properties of the higher moment tensors. The paper by Ghalanos et al (2013) contains more specific details.
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 AR/VAR mean forecast).

Author(s)

Alexios Galanos

References

Chen, Y., Hardle, W., and Spokoiny, V. 2010, GHICA-Risk analysis with GH distributions and independent components, Journal of Empirical Finance, 17(2), 255–269.
de Athayde, G.M. and Flores Jr, R.G. 2002, On Certain Geometric Aspects of Portfolio Optimisation with Higher Moments, mimeo.
Ghalanos, A., Rossi, E., and Urga, G. (2013). Independent Factor Autoregressive Conditional Density Model, forthcoming.
Paolella, M.S. 2007, Intermediate Probability - A Computational Approach, Wiley-Interscience.

class: GO-GARCH Roll Class

Description

Class for the GO-GARCH Roll.

Objects from the Class

The class is returned by calling the function gogarchroll.

Slots

forecast:

Object of class "vector" which contains the rolling forecasts of the distributional parameters for each factor.

model:

Object of class "vector" containing details of the GOGARCH model specification.

Extends

Class "mGARCHroll", directly. Class "GARCHroll", by class "mGARCHroll", distance 2. Class "rGARCH", by class "mGARCHroll", distance 3.

Methods

coef

signature(object = "goGARCHroll"): Extraction of independent factor GARCH model coefficients saved from the goGARCHfit objects(returns a list).

fitted

signature(object = "goGARCHroll"): Extracts the conditional fitted forecast values (returns an xts object with index the actual forecast T+1 times).

sigma

signature(object = "goGARCHroll"): Extracts the conditional sigma forecast values (returns an xts object with index the actual forecast T+1 times). Takes optional argument “factors” (default TRUE) denoting whether to return the factor conditional sigma or the transformed sigma for the assets.

rcov

signature(object = "goGARCHroll"): Returns the time-varying n.asset x n.asset x (n.roll+1) covariance matrix in array format, where the third dimension labels are now the actual rolling n.ahead=1 forecast time indices (T+1). A further argument ‘output’ allows to switch between “array” and “matrix” returned object.

rcor

signature(object = "goGARCHroll"): Returns the time-varying n.asset x n.asset x (n.roll+1) correlation matrix in array format, where the third dimension labels are now the actual rolling n.ahead=1 forecast time indices (T+1). A further argument ‘output’ allows to switch between “array” and “matrix” returned object.

rcoskew

signature(object = "goGARCHroll"): Returns the time-varying n.asset x n.asset^2 x (n.roll+1) coskewness matrix in array format, where the third dimension labels are now the actual rolling n.ahead=1 forecast time indices (T+1). There is a “standardize” option which indicates whether the coskewness should be standardized by the conditional sigma (see equations in vignette).

rcokurt

signature(object = "goGARCHroll"): Returns the time-varying n.asset x n.asset^3 x (n.roll+1) cokurtosis matrix in array format, where the third dimension labels are now the actual rolling n.ahead=1 forecast time indices (T+1). There is a “standardize” option which indicates whether the cokurtosis should be standardized by the conditional sigma (see equations in vignette).

gportmoments

signature(object = "goGARCHroll"):
function:
gportmoments(object, weights)
Calculates the first 4 standardized portfolio moments using the geometric properties of the model, given a matrix of asset weights with row dimension equal to the total rolling forecast horizon. Returns an xts object of dimensions (total rolling forecast) x 4 (moments), with the index denoting the T+1 actual forecast time. If the number of assets > 100, then the kurtosis is not returned (see cokurtosis restrictions below).

convolution

signature(object = "goGARCHroll"):
function:
convolution(object, weights, fft.step = 0.001, fft.by = 0.0001, fft.support = c(-1, 1), support.method = c("user", "adaptive"), use.ff = TRUE, cluster = NULL, trace = 0,...)
The convolution method takes a goGARCHroll 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 total forecast horizon. 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. The option for parallel computation is available via the use of a cluster object as elsewhere in this package. Passing this object to the distribution methods (e.g. qfft) follows the same rules as the goGARCHforecast object, namely that the index is zero based.

show

signature(object = "goGARCHroll"): Summary.

Author(s)

Alexios Galanos

class: GO-GARCH Simultion Class

Description

Class for the GO-GARCH Simulation.

Objects from the Class

The class is returned by calling the function gogarchsim.

Slots

msim:

Object of class "vector" The multivariate simulation list.

model:

Object of class "vector" containing details of the GOGARCH model specification.

Extends

Class "mGARCHsim", directly. Class "GARCHsim", by class "mGARCHsim", distance 2. Class "rGARCH", by class "mGARCHsim", distance 3.

Methods

convolution

signature(object = "goGARCHsim"):
function:
convolution(object, weights, fft.step = 0.001, fft.by = 0.0001, fft.support = c(-1, 1), support.method = c("user", "adaptive"), use.ff = TRUE, sim = 1, cluster = NULL, trace = 0,...)
The convolution method takes a goGARCHsim object and a weights vector and calculates the weighted density. The vector must be the same length as the number of assets. The “sim” option indicates the simulation index to use, given the “m.sim” option chosen in the call to the simulation function. 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 use of the “ff” package returning instead a list. Finally, the option for parallel computation is available via the use of a cluster object as elsewhere in this package.

gportmoments

signature(object = "goGARCHsim"):
function:
gportmoments(object, weights, sim = 1)
Calculates the first 3 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 “sim” option indicates the simulation index to use, given the “m.sim” option chosen in the call to the simulation function.

rcoskew

signature(object = "goGARCHsim"):
function:
rcoskew(object, from = 1, to = 1, sim = 1)
Returns the 'time-varying' NxN^2 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. The “sim” option indicates the simulation index to use, given the “m.sim” option chosen in the call to the simulation function.

rcokurt

signature(object = "goGARCHsim"):
function:
rcokurt(object, standardize = TRUE, from = 1, to = 1)
Returns the 'time-varying' NxN^3 cokurtosis 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 models with less than 20 assets.

rcov

signature(object = "goGARCHsim"): Returns the time-varying NxN covariance matrix in array format. There is an additional “sim” option which indicates the simulation index to use, given the “m.sim” option chosen in the call to the simulation function. A further argument ‘output’ allows to switch between “array” and “matrix” returned object.

rcor

signature(object = "goGARCHsim"): Returns the time-varying NxN correlation matrix in array format. There is an additional “sim” option which indicates the simulation index to use, given the “m.sim” option chosen in the call to the simulation function. A further argument ‘output’ allows to switch between “array” and “matrix” returned object.

as.matrix

signature(x = "goGARCHsim"):
function:
as.matrix(x, which = "A")
This returns four types of matrices relating to the estimation of the independent components in the GO-GARCH model. Valid choices are “A” for the mixing matrix, “W” for the unmixing matrix, “U” for the rotational matrix and “K” for the whitening matrix, “Kinv” for the de-whitening matrix.

Author(s)

Alexios Galanos

class: GO-GARCH Specification Class

Description

Class for the GO-GARCH specification.

Objects from the Class

The class is returned by calling the function goGARCHspec.

Slots

model:

Multivariate model specification.

umodel:

Univariate model specification.

Extends

Class "mGARCHspec", directly. Class "GARCHspec", by class "mGARCHspec", distance 2. Class "rGARCH", by class "mGARCHspec", distance 3.

Methods

show

signature(object = "goGARCHspec"): Summary method.

Note

The mixing matrix in the GO-GARCH model implemented in the rmgarch package is based on non-parametric independent component analysis (ICA) methodology. The estimation is a 2-stage methodology described in Broda and Paolella (2009) and Zhang and Chan (2009). The extension to the use of the full multivariate affine GH distribution is detailed in Ghalanos et al (2011).

Author(s)

Alexios Galanos

References

van der Weide, R. 2002, GO-GARCH: a multivariate generalized orthogonal GARCH model, Journal of Applied Econometrics, 549–564.
Zhang, K. and Chan, L. 2009, Efficient factor GARCH models and factor-DCC models, Quantitative Finance, 71–91.
Broda, S.A. and Paolella, M.S. 2009, CHICAGO: A Fast and Accurate Method for Portfolio Risk Calculation, Journal of Financial Econometrics, 412–436.
Ghalanos, A. and Rossi, E. and Urga, G. 2011, Independent Factor Autoregressive Conditional Density Model, Pending–submitted.

function: GO-GARCH Filter

Description

Method for filtering the GO-GARCH model.

Usage

gogarchfilter(fit, data, out.sample = 0, n.old = NULL, cluster = NULL, ...) 

Arguments

Value

A goGARCHfilter object containing details of the GO-GARCH filter.

Author(s)

Alexios Galanos

Examples

## Not run: 
data(dji30ret)
spec = gogarchspec()
fit = gogarchfit(spec = spec, data = dji30ret[,1:4], gfun = "tanh")
filter = gogarchfilter(fit, data = dji30ret[,1:4])

## End(Not run)

function: GO-GARCH Filter

Description

Method for filtering the GO-GARCH model.

Usage

gogarchfit(spec, data, out.sample = 0, solver = "solnp", 
fit.control = list(stationarity = 1), solver.control = list(), cluster = NULL, 
VAR.fit = NULL, ARcoef = NULL, ...) 

Arguments

Value

A goGARCHfit object containing details of the GO-GARCH fit.

Note

There is no check on the VAR.fit list passed to the method so particular care should be exercised so that the same data used in the fitting routine is also used in the VAR filter routine. The ability to pass this list of the pre-calculated VAR model is particularly useful when comparing different models (such as copula GARCH, DCC GARCH etc) using the same dataset and VAR method. Though the classical VAR estimation is very fast and may not require this extra step, the robust method is slow and therefore benefits from calculating this only once.

Author(s)

Alexios Galanos

Examples

## Not run: 
data(dji30ret)
spec = gogarchspec(mean.model = list(demean = "constant"), 
variance.model = list(model = "sGARCH", garchOrder = c(1,1), submodel = NULL), 
distribution.model = list(distribution = "manig"),ica = "fastica")

fit = gogarchfit(spec = spec, data  = dji30ret[,1:4, drop = FALSE], 
out.sample = 50, gfun = "tanh")
fit

## End(Not run)

function: GO-GARCH Forecast

Description

Method for forecasting from the GO-GARCH model.

Usage

gogarchforecast(fit, n.ahead = 10, n.roll = 0, 
external.forecasts = list(mregfor = NULL), cluster = NULL, ...) 

Arguments

Value

A goGARCHforecast object containing details of the GO-GARCH forecast.

Author(s)

Alexios Galanos

Examples

## Not run: 
data(dji30ret)
spec = gogarchspec()
fit = gogarchfit(spec = spec, data = dji30ret[,1:4], out.sample = 10, 
gfun = "tanh")
forecast = gogarchforecast(fit, n.ahead = 1, n.roll = 9)

## End(Not run)

function: GO-GARCH Rolling Estimation

Description

Method for performing rolling estimation of the GO-GARCH model.

Usage

gogarchroll(spec, data, n.ahead = 1, forecast.length = 50, n.start = NULL, 
refit.every = 25, refit.window = c("recursive", "moving"), window.size = NULL, 
solver = "solnp", solver.control = list(), fit.control = list(), rseed = NULL,  
cluster = NULL, save.fit = FALSE, save.wdir = NULL, ...)

Arguments

Value

An object of class goGARCHroll.

Author(s)

Alexios Galanos

function: GO-GARCH Simulation

Description

Method for simulation from a fitted GO-GARCH model.

Usage

gogarchsim(object, n.sim = 1, n.start = 0, m.sim = 1,
startMethod = c("unconditional", "sample"), prereturns = NA, preresiduals = NA,
presigma = NA, mexsimdata = NULL, rseed = NULL, cluster = NULL, ...)

Arguments

Value

A goGARCHsim object containing details of the GO-GARCH simulation.

Author(s)

Alexios Galanos

function: GO-GARCH Specification

Description

Method for creating a GO-GARCH specification object prior to fitting.

Usage

gogarchspec(mean.model = list(model = c("constant", "AR", "VAR"), robust = FALSE, 
lag = 1, lag.max = NULL, lag.criterion = c("AIC", "HQ", "SC", "FPE"), 
external.regressors = NULL, 
robust.control = list("gamma" = 0.25, "delta" = 0.01, "nc" = 10, "ns" = 500)), 
variance.model = list(model = "sGARCH", garchOrder = c(1,1), submodel = NULL, 
variance.targeting = FALSE), distribution.model = c("mvnorm", "manig", "magh"), 
ica = c("fastica", "radical"), 
ica.fix = list(A = NULL, K = NULL), ...) 

Arguments

Value

A goGARCHspec object containing details of the GO-GARCH specification.

Author(s)

Alexios Galanos

Load Scenario from File

Description

Loads a previously saved fScenario from file and returns a fScenario or fMoments object.

Usage

goload(object, ...)

Arguments

Details

There are times when it is more efficient to save large scenarios to file (particularly when creating them in parallel), rather than returning them to the user workspace. The save.output option in the fscenario and fmoments allows to do just that, returning instead a lighter object with an empty scenario slot, but with the model slot included, containing the details of the location and name of the saved scenario (or moments list). The goload function then takes this object, reads the location and name and loads the scenario (or moments) into its slot in the object and returns this to the user's workspace.

Value

A fScenario or fMoments object with the scenario or moments slot now filled with the saved data from file.

Author(s)

Alexios Galanos

First and Last methods for accessing objects

Description

Functions for accessing first-n and last-n values of an object (similar to head and tail).

Usage

last(x, index = 1, ...)
first(x, index = 1, ...)

Arguments

Methods

signature(x = "ANY")

signature(x = "array")

Author(s)

Alexios Galanos

Class: Multivariate GARCH Filter Class

Description

High Level multivariate GARCH filter class.

Objects from the Class

A virtual Class: No objects may be created from it.

Extends

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

Methods

No methods defined with class "mGARCHfilter" in the signature.

Author(s)

Alexios Galanos

Class: Multivariate GARCH Fit Class

Description

High Level multivariate GARCH fit class.

Objects from the Class

A virtual Class: No objects may be created from it.

Extends

Class "GARCHfit", directly. Class "rGARCH", by class "GARCHfit", distance 2.

Methods

No methods defined with class "mGARCHfit" in the signature.

Author(s)

Alexios Galanos

Class: Multivariate GARCH Forecast Class

Description

High Level multivariate GARCH forecast class.

Objects from the Class

A virtual Class: No objects may be created from it.

Extends

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

Methods

No methods defined with class "mGARCHforecast" in the signature.

Author(s)

Alexios Galanos

Class: Multivariate GARCH Roll Class

Description

High Level multivariate GARCH roll class.

Objects from the Class

A virtual Class: No objects may be created from it.

Extends

Class "GARCHroll", directly. Class "rGARCH", by class "GARCHroll", distance 2.

Methods

No methods defined with class "mGARCHroll" in the signature.

Author(s)

Alexios Galanos

Class: Multivariate GARCH Simulation Class

Description

High Level multivariate GARCH simulation class.

Objects from the Class

A virtual Class: No objects may be created from it.

Extends

Class "GARCHsim", directly. Class "rGARCH", by class "GARCHsim", distance 2.

Methods

No methods defined with class "mGARCHsim" in the signature.

Author(s)

Alexios Galanos

Class: Multivariate GARCH Specification

Description

High Level multivariate GARCH specification class.

Objects from the Class

A virtual Class: No objects may be created from it.

Extends

Class "GARCHspec", directly. Class "rGARCH", by class "GARCHspec", distance 2.

Methods

No methods defined with class "mGARCHspec" in the signature.

Author(s)

Alexios Galanos

The Robust Accurate, Direct ICA aLgorithm (RADICAL).

Description

An ICA algorithm based on an efficient entropy estimator (due to Vasicek) which is robust to outliers.

Usage

radical(X, n.comp = dim(X)[2], demean = TRUE, pca.cov = c("ML", "LW", "ROB", "EWMA"), 
k = 150, augment = FALSE, replications = 30, sd = 0.175, firstEig = 1, 
lastEig = dim(X)[1], pcaE = NULL, pcaD = NULL, whiteSig = NULL, whiteMat = NULL, 
dewhiteMat = NULL, rseed = NULL, trace = FALSE, ...)

Arguments

Details

The interested reader should consult the paper in the references section for details on the properties of the algorithm.
The algorithm is quite slow, despite partial implementation in C++, and should only be used on small to medium sized sets.

Value

A list containing the following values:

Author(s)

Erik G. Learned-Miller for the Radical algorithm and Matlab package.
Alexios Galanos for this R-port.

References

Learned-Miller, A.G and Fisher III, J.W., 2003, ICA Using Spacings Estimates of Entropy, Journal of Machine Learning Research, 4, 1271-1295. http://www.cs.umass.edu/~elm/ICA/

Examples

## Not run: 
# create a set of independent signals S, glued together by a mixing matrix A
# (note the notation and matrix multiplication direction as we are dealing with
# row rather than column vectors)
set.seed(100)
S <- matrix(runif(10000), 5000, 2)
A <- matrix(c(1, 1, -1, 2), 2, 2, byrow = TRUE)
# the mixed signal X
X = S %*% t(A)
# The function centers and whitens (by the eigenvalue decomposition of the 
# unconditional covariance matrix) the data before applying the theICA algorithm.
IC <- radical(X, n.comp = 2)

# demeaned data:
X_bar = scale(X, scale = FALSE)

# whitened data:
X_white = X_bar %*% t(IC$whiteningMatrix)

# check whitening:
# check correlations are zero
cor(X_white)
# check diagonals are 1 in covariance
cov(X_white)

# check that the estimated signals(S) multiplied by the
# estimated mxing matrix (A) are the same as the original dataset (X)
round(head(IC$S %*% t(IC$A)), 12) == round(head(X), 12)

# do some plots:
par(mfrow = c(1, 3))
plot(IC$S %*% t(IC$A), main = "Pre-processed data")
plot(X_white, main = "Whitened and Centered components")
plot(IC$S, main = "ICA components")

## End(Not run)

VARX Fit/Filter/Forecast/Simulation Functions

Description

Vector Autoregressive (VAR) with Constant and Optional Exogenous Regressors (X) Fit, Filter, Forecast and Simulation functions for use with multivariate GARCH models.

Usage

varxfit(X, p, constant = TRUE, exogen = NULL, robust = FALSE, gamma = 0.25, 
delta = 0.01, nc = 10, ns = 500, postpad = c("none", "constant", "zero", "NA"), 
cluster = NULL)
varxfilter(X, p, Bcoef, exogen = NULL, postpad = c("none", "constant", "zero", "NA"))
varxforecast(X, Bcoef, p, out.sample, n.ahead, n.roll, mregfor)
varxsim (X, Bcoef, p, n.sim, n.start, prereturns, resids, mexsimdata)

Arguments

Details

This are convenience functions to be optionally used when using the multivariate GARCH methods.

Value

A list with the following items:

The varxsim returns an n.sim x n.asset matrix of the simulated conditional means, while the varxforecast returns an n.ahead x n.assets x (n.roll+1) array of the forecast conditional means.

Note

Part of the varxfit functionality and structure is inspired from the 'vars' package, but the estimation method is implemented in a very quick way without calling 'lm'. The robust method is based on the matlab program of Christophe Croux available from his website and the option of using parallel computation is implemented for this particular choice.The postpad option is used when the returned data needs to be of the same size as the inputed data for easier manipulation/comparison (since padding is done post-estimation, there is no bias introduced during estimation).

Author(s)

Alexios Galanos

References

Lutkepohl, H. 2005, New introduction to multiple time series analysis, Springer.
Croux, C. and Joossens, K. 2008, Robust estimation of the vector autoregressive model by a least trimmed squares procedure, COMPSTAT, 489–501.

Weighted Distribution Margin

Description

Return the weighted margin of one of 3 elliptical distributions given a matrix of weights.

Usage

wmargin(distribution = "mvnorm", weights, mean, Sigma, shape = NA, skew = NA)

Arguments

Details

This is just a convenience function to return the weighted variance and mean of the three elliptical distributions given a set of weights.

Value

A matrix with each row representing the conditional weighted marginal density with corresponding parameters.

Author(s)

Alexios Galanos