Dow Jones Industrial Average and Nasdaq stock indices

Description

Levels of the Dow Jones Industrial Average and NASDAQ stock indices for the period 03/23/1990 until 03/23/2000.

Usage

data(BVDW)

Format

A data frame with 2610 observations on the following 3 variables.

Date

Date in the format YYYYMMDD.

DJIA

Level of the DIJA.

NASDAQ

Level of the NASDAQ.

Details

This data set has been utilized in the source below and was kindly provided by Roy van der Weide.

Source

Boswijk, H. Peter and van der Weide, Roy (2006), Wake me up before you GO-GARCH, Tinbergen Institute Discussion Paper, TI 2006-079/4, University of Amsterdam and Tinbergen Institute.

See Also

VDW

Examples

data(BVDW)
str(BVDW)

Stock prices transportation sector, oil and kerosene prices

Description

This data frame contains the stock prices from American Airlines, South-West Airlines, Boeing and FedEx. In addition the spot prices for crude oil and kerosene are included. This data set was used in the article by Boswijk and van der Weide (2009). The data range is from July, 19 1993 until August, 12 2008.

Usage

data(BVDWAIR)

Format

A data frame with 3791 observations on the following 7 variables.

Date

POSIXt: The dates of observations.

CrudeOil

Crude oil price.

Kerosene

Kerosene price.

AmericanAir

Stock prices of American Airlines.

SouthWest

Stock prices of South-West Airlines.

Boeing

Stock prices of Boeing.

FedEx

Stock prices of Boeing.

Details

The stock price data was downloaded from Yahoo Finance and the price series for crude oil and kerosene were obtained from the U.S. Energy Information Administration (EIA).

Source

http://www.econstats.com

References

Boswijk, H. Peter and van der Weide, Roy (2009), Method of Moments Estimation of GO-GARCH Models, Working Paper, University of Amsterdam, Tinbergen Institute and World Bank.

Examples

data(BVDWAIR)
str(BVDWAIR)

Sector indices of the EURO STOXX 600

Description

The data frame contains the following sector indices of the EURO STOXX 600 index: Automobiles \& Parts, Banks, Basic Resources, Chemicals, Construction and Materials, Financial Services, Food \& Beverages, Health Care, Industrial Goods \& Services, Insurance, Media, Oil \& Gas, Technology, Telecommunications and Utilities. The data range is from 31th December 1986 until 21st November 2008.

Usage

data(BVDWSTOXX)

Format

A data frame with 5652 observations on the following 16 variables.

Date

POSIXt: The dates of observations.

AutoParts

Sector index Automobiles \& Parts

Banks

Sector index Banks

BasicRes

Sector index Basic Resources

Chemicals

Sector index Chemicals

ConstrMat

Sector index Construction and Materials

FoodBeverage

Sector index Food \& Beverages

FinService

Sector index Financial Services

HealthCare

Sector index Health Care

IndustrialGoods

Sector index Industrial Goods \& Services

Insurance

Sector index Insurance

Media

Sector index Media

OilGas

Sector index Oil \& Gas

Technology

Sector index Technology

Telecom

Sector index Telecommunications

Utilities

Sector index Utilities

Source

http://www.stoxx.com

References

Boswijk, H. Peter and van der Weide, Roy (2009), Method of Moments Estimation of GO-GARCH Models, Working Paper, University of Amsterdam, Tinbergen Institute and World Bank.

Examples

data(BVDWSTOXX)
str(BVDWSTOXX)

Class "GoGARCH": Estimated GO-GARCH Models

Description

This class defines the slots for estimated GO-GARCH models. It contains the class Goinit.

Objects from the Class

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

Slots

Z:

Object of class "matrix": Transformation matrix.

U:

Object of class "Orthom": Orthonormal matrix.

Y:

Object of class "matrix": Extracted component matrix.

H:

Object of class "list": List of conditional variance/covariance matrices.

models:

Object of class "list": List of univariate GARCH model fits.

estby:

Object of class "character": Estimation method.

CALL:

Object of class "call": Result of match.call in generating function.

X:

Object of class "matrix": The data matrix.

V:

Object of class "matrix": Covariance matrix of X.

P:

Object of class "matrix": Left singular values of Var/Cov matrix of X.

Dsqr:

Object of class "matrix": Square roots of eigenvalues on diagonal, else zero.

garchf:

Object of class "formula": Garch formula used for uncorrelated component GARCH models.

name:

Object of class "character": The name of the original data object.

Extends

Class "Goinit", directly.

Methods

cvar

Returns the conditional variances as object with class attribute "mts" "ts".

ccov

Returns the conditional co-variances as object with class attribute "mts" "ts".

ccor

Returns the conditional correlationsas object with class attribute "mts" "ts".

coef

Returns the coeffiecients of the component GARCH models.

converged

Returns the convergence codes of the component GARCH models.

formula

Returns the formula for the component GARCH models.

plot

Plotting of the conditional correlations.

predict

Returns the conditional covariances and mean forecasts and the forecasts of the component GARCH models, object is of class Gopredict.

residuals

Returns the residuals of the GO-GARCH model.

show

show-method for objects of class GoGARCH.

summary

summary-method for objects of class GoGARCH, object is of class Gosum.

update

Updates an object of class GoGARCH.

Author(s)

Bernhard Pfaff

See Also

Goinit, Gosum, Gopredict

Class "Goestica": GO-GARCH models estimated by fast ICA

Description

This class contains the GoGARCH class and has the mixing matrix A as additional slot.

Objects from the Class

Objects can be created by calls of the form new("Goestmm", ...), or with the function gogarch whereby method = "ica" has been set.

Slots

ica:

Object of class "list": List object returned by fastICA.

Z:

Object of class "matrix": Transformation matrix.

U:

Object of class "matrix": Orthogonal matrix.

Y:

Object of class "matrix": Extracted component matrix.

H:

Object of class "list": List of conditional variance/covariance matrices.

models:

Object of class "list": List of univariate GARCH model fits.

estby:

Object of class "character": Estimation method.

X:

Object of class "matrix": The data matrix.

V:

Object of class "matrix": Covariance matrix of X.

P:

Object of class "matrix": Left singular values of Var/Cov matrix of X.

Dsqr:

Object of class "matrix": Square roots of eigenvalues on diagonal, else zero.

garchf:

Object of class "formula": Garch formula used for uncorrelated component GARCH models.

name:

Object of class "character": The name of the original data object.

Extends

Class "GoGARCH", directly. Class "Goinit", by class "GoGARCH", distance 2.

Methods

cvar

Returns the conditional variances as object with class attribute "mts" "ts".

ccov

Returns the conditional co-variances as object with class attribute "mts" "ts".

ccor

Returns the conditional correlationsas object with class attribute "mts" "ts".

coef

Returns the coeffiecients of the component GARCH models.

converged

Returns the convergence codes of the component GARCH models.

formula

Returns the formula for the component GARCH models.

goest

Fast ICA estimation of Go-GARCH models.

plot

Plotting of the conditional correlations.

predict

Returns the conditional covariances and mean forecasts and the forecasts of the component GARCH models, object is of class Gopredict.

residuals

Returns the residuals of the Go-GARCH model as object with class attribute "mts" "ts".

resid

Returns the residuals of the Go-GARCH model as object with class attribute "mts" "ts".

show

show-method for objects of class Goestmm.

summary

summary-method for objects of class Goestml, object is of class Gosum.

update

Updates an object of class Goestml.

Author(s)

Bernhard Pfaff

References

Broda, S.A. and Paolella, M.S. (2008): CHICAGO: A Fast and Accurate Method for Portfolio Risk Calculation, Swiss Finance Institute, Research Paper Series No. 08-08, Zuerich.

See Also

GoGARCH, Goinit, Gosum, Gopredict, goest-methods and gogarch

Class "Goestml": GO-GARCH models estimated by Maximum-Likelihood

Description

This class contains the GoGARCH class and has the outcome of nlminb as an additional slot.

Objects from the Class

Objects can be created by calls of the form new("Goestml", ...), or with the function gogarch whereby method = "ml" has been set.

Slots

opt:

Object of class "list": List returned by nlminb.

Z:

Object of class "matrix": Transformation matrix.

U:

Object of class "matrix": Orthogonal matrix.

Y:

Object of class "matrix": Extracted component matrix.

H:

Object of class "list": List of conditional variance/covariance matrices.

models:

Object of class "list": List of univariate GARCH model fits.

estby:

Object of class "character": Estimation method.

X:

Object of class "matrix": The data matrix.

V:

Object of class "matrix": Covariance matrix of X.

P:

Object of class "matrix": Left singular values of Var/Cov matrix of X.

Dsqr:

Object of class "matrix": Square roots of eigenvalues on diagonal, else zero.

garchf:

Object of class "formula": Garch formula used for uncorrelated component GARCH models.

name:

Object of class "character": The name of the original data object.

Extends

Class "GoGARCH", directly. Class "Goinit", by class "GoGARCH", distance 2.

Methods

angles

Returns the Eulerian angles.

cvar

Returns the conditional variances as object with class attribute "mts" "ts".

ccov

Returns the conditional co-variances as object with class attribute "mts" "ts".

ccor

Returns the conditional correlations as object with class attribute "mts" "ts".

coef

Returns the coeffiecients of the component GARCH models.

converged

Returns the convergence codes of the component GARCH models.

formula

Returns the formula for the component GARCH models.

goest

ML-Estimation of Go-GARCH models.

logLik

Returns the value of the log-Likelihood function.

plot

Plotting of the conditional correlations.

predict

Returns the conditional covariances and mean forecasts and the forecasts of the component GARCH models, object is of class Gopredict.

residuals

Returns the residuals of the Go-GARCH model as object with class attribute "mts" "ts".

resid

Returns the residuals of the Go-GARCH model as object with class attribute "mts" "ts".

show

show-method for objects of class Goestml.

summary

summary-method for objects of class Goestml, object is of class Gosum.

update

Updates an object of class Goestml.

Author(s)

Bernhard Pfaff

See Also

GoGARCH, Goinit, Gosum, Gopredict, goest-methods

Class "Goestmm": Go-GARCH models estimated by Methods of Moments

Description

This class contains the GoGARCH class and has the weights vector and the matched orthogonal matrices U as additional slots.

Objects from the Class

Objects can be created by calls of the form new("Goestmm", ...), or with the function gogarch whereby method = "mm" has been set.

Slots

weights:

Object of class "numeric": Weights for aggregating the matched orthogonal matrices U.

Umatched:

Object of class "list": List of matched orthogonal matrices U.

Z:

Object of class "matrix": Transformation matrix.

U:

Object of class "matrix": Orthogonal matrix.

Y:

Object of class "matrix": Extracted component matrix.

H:

Object of class "list": List of conditional variance/covariance matrices.

models:

Object of class "list": List of univariate GARCH model fits.

estby:

Object of class "character": Estimation method.

X:

Object of class "matrix": The data matrix.

V:

Object of class "matrix": Covariance matrix of X.

P:

Object of class "matrix": Left singular values of Var/Cov matrix of X.

Dsqr:

Object of class "matrix": Square roots of eigenvalues on diagonal, else zero.

garchf:

Object of class "formula": Garch formula used for uncorrelated component GARCH models.

name:

Object of class "character": The name of the original data object.

Extends

Class "GoGARCH", directly. Class "Goinit", by class "GoGARCH", distance 2.

Methods

cvar

Returns the conditional variances as object with class attribute "mts" "ts".

ccov

Returns the conditional co-variances as object with class attribute "mts" "ts".

ccor

Returns the conditional correlationsas object with class attribute "mts" "ts".

coef

Returns the coeffiecients of the component GARCH models.

converged

Returns the convergence codes of the component GARCH models.

formula

Returns the formula for the component GARCH models.

goest

Methods of moments estimation of Go-GARCH models.

plot

Plotting of the conditional correlations.

predict

Returns the conditional covariances and mean forecasts and the forecasts of the component GARCH models, object is of class Gopredict.

residuals

Returns the residuals of the Go-GARCH model as object with class attribute "mts" "ts".

resid

Returns the residuals of the Go-GARCH model as object with class attribute "mts" "ts".

show

show-method for objects of class Goestmm.

summary

summary-method for objects of class Goestml, object is of class Gosum.

update

Updates an object of class Goestml.

Author(s)

Bernhard Pfaff

References

Boswijk, H. Peter and van der Weide, Roy (2009), Method of Moments Estimation of GO-GARCH Models, Working Paper, University of Amsterdam, Tinbergen Institute and World Bank.

See Also

GoGARCH, Goinit, Gosum, Gopredict, goest-methods, gogarch, Umatch

Class "Goestnls": GO-GARCH models estimated by Non-linear Least-Squares

Description

This class contains the GoGARCH class and has the outcome of optim as an additional slot.

Objects from the Class

Objects can be created by calls of the form new("Goestnls", ...), or with the function gogarch whereby method = "nls" has been set.

Slots

nls:

Object of class "list": List returned by optim.

Z:

Object of class "matrix": Transformation matrix.

U:

Object of class "matrix": Orthogonal matrix.

Y:

Object of class "matrix": Extracted component matrix.

H:

Object of class "list": List of conditional variance/covariance matrices.

models:

Object of class "list": List of univariate GARCH model fits.

estby:

Object of class "character": Estimation method.

X:

Object of class "matrix": The data matrix.

V:

Object of class "matrix": Covariance matrix of X.

P:

Object of class "matrix": Left singular values of Var/Cov matrix of X.

Dsqr:

Object of class "matrix": Square roots of eigenvalues on diagonal, else zero.

garchf:

Object of class "formula": Garch formula used for uncorrelated component GARCH models.

name:

Object of class "character": The name of the original data object.

Extends

Class "GoGARCH", directly. Class "Goinit", by class "GoGARCH", distance 2.

Methods

cvar

Returns the conditional variances as object with class attribute "mts" "ts".

ccov

Returns the conditional co-variances as object with class attribute "mts" "ts".

ccor

Returns the conditional correlationsas object with class attribute "mts" "ts".

coef

Returns the coeffiecients of the component GARCH models.

converged

Returns the convergence codes of the component GARCH models.

formula

Returns the formula for the component GARCH models.

goest

NLS-Estimation of Go-GARCH models.

plot

Plotting of the conditional correlations.

predict

Returns the conditional covariances and mean forecasts and the forecasts of the component GARCH models, object is of class Gopredict.

residuals

Returns the residuals of the Go-GARCH model as object with class attribute "mts" "ts".

resid

Returns the residuals of the Go-GARCH model as object with class attribute "mts" "ts".

show

show-method for objects of class Goestnls.

summary

summary-method for objects of class GoGARCH, object is of class Gosum.

update

Updates an object of class GoGARCH.

Author(s)

Bernhard Pfaff

See Also

GoGARCH, Goinit, Gosum, Gopredict, goest-methods, gogarch

Class "Goinit": Initialisation of GO-GARCH models

Description

This class defines the required slots for estimating GO-GARCH models.

Objects from the Class

Objects can be created by calls of the form new("Goinit", ...), or more conveniently by goinit().

Slots

X:

Object of class "matrix": The data matrix.

V:

Object of class "matrix": Covariance matrix of X.

P:

Object of class "matrix": Left singular values of Var/Cov matrix of X.

Dsqr:

Object of class "matrix": Square roots of eigenvalues on diagonal, else zero.

garchf:

Object of class "formula": Garch formula used for uncorrelated component GARCH models.

name:

Object of class "character": The name of the original data object.

Methods

show

Prints the slots, whereby for X only the head is displayed.

Author(s)

Bernhard Pfaff

See Also

garchFit, goinit

Examples

showClass("Goinit")

Class "Gopredict": Prediction of GO-GARCH Models

Description

This class defines the slots for forecasts from a GO-GARCH model.

Objects from the Class

Objects can be created by calls of the form new("Gopredict", ...), or with the method predict of formal class objects GoGARCH and Goestml.

Slots

Hf:

Object of class "list": The forecasted conditional covariances.

Xf:

Object of class "matrix": The transformed forecasts of the component GARCH mean models.

CGARCHF:

Object of class "list": The original forecasts of the component GARCH models.

Methods

ccor

Returns the forecasted conditional correlations.

ccov

Returns the forecasted conditional co-variances.

cvar

Returns the forecasted conditional variances.

show

show-method for objects of class Gopredict.

Note

In case more than 10 forecasts steps are computed, the show-method displays only the head of the returned objects. Furthermore, the show-method displays the forecasted conditional variances only. The forecasted conditional co-variances and/or the forecasted conditional correlations can be retrieved with the methods ccov or ccor, respectively.

Author(s)

Bernhard Pfaff

See Also

GoGARCH, Goestml

Class "Gosum": Summary object of GO-GARCH model

Description

The formal summary class of GoGARCH objects or objects that extend this class.

Objects from the Class

Objects can be created by calls of the form new("Gosum", ...) or are set by the summary-method.

Slots

name:

character: the name of the original data object.

method:

character: the estimation method.

model:

formula: The GARCH model formula for the component GARCH models.

garchc:

list: The elements are matcoef matrices generated by garchFit for the components.

Zinv:

matrix: The inverse of the linear map X = Y Z.

Methods

show

show-method for objects of class Gosum.

Author(s)

Bernhard Pfaff

See Also

GoGARCH, Goestml

Class "Orthom": Orthogonal matrices

Description

This class defines an orthogonal matrix, which is characterized by det(M) = 1 and M M' = I.

Objects from the Class

Objects can be created by calls of the form new("Orthom", ...). In addition the function UprodR returns an object of formal class Orthom.

Slots

M:

Object of class "matrix".

Methods

M

Returns the slot M of class Orthom.

print

print-method for objects of class Orthom.

show

show-method for objects of class Orthom.

t

Transpose of object@M.

Note

Objects are validated by validOrthomObject(). This function is utilised by validObject().

Author(s)

Bernhard Pfaff

See Also

UprodR, validOrthomObject

Examples

showClass("Orthom")

Rotation matrix, 2-dimensional

Description

Given an angle \theta whereby \theta \in [0, \pi/2) the function Rd2 returns a 2-dimensional rotation matrix of Euler angles.

Usage

Rd2(theta)

Arguments

Value

Author(s)

Bernhard Pfaff

See Also

UprodR

Examples

Rd2(pi/3)

Matching of Orthogonal Matrices for Cayley transforms

Description

This function matches an orthogonal matrix to the importance of the columns of the matrix to which it should be matched.

Usage

Umatch(from, to)

Arguments

Value

Author(s)

Bernhard Pfaff

References

Boswijk, H. Peter and van der Weide, Roy (2009), Method of Moments Estimation of GO-GARCH Models, Working Paper, University of Amsterdam, Tinbergen Institute and World Bank.

Liebeck, H. and Osborne, A. (1991), The Generation of All Rational Orthogonal Matrices, The American Mathematical Monthly, 98 (2) (Feb. 1991), 131 – 133.

See Also

gogarch

Creation of an orthogonal matrix

Description

This function returns an orthogonal matrix which results of the matrix products of rotation matrices.

Usage

UprodR(theta)

Arguments

Details

The length of theta must be equal to m * (m - 1) / 2, where m is the dimension of the orthogonal matrix. The elements of theta must lie in the interval [0, \pi/2).

Value

Author(s)

Bernhard Pfaff

References

Vilenkin, N. Ja. (1968), Special Functions and the Theory of Group Representations, Translations of Mathematical Monographs, 22, American Math. Soc., Providence, Rhode Island, USA.

See Also

Rd2, Orthom

Examples

theta <- c(pi/3, pi/5, pi/7)
U <- UprodR(theta)
U

Dow Jones Industrial Average and Nasdaq stock indices

Description

The daily (log) returns of the Dow Jones Industrial Average and the NASDAQ composite, respectively. The daily observations start at the first of January, 1990, and end in October 2001.

Usage

data(VDW)

Format

A data frame with 3082 observations on the following 2 variables.

DJIA

Log-return of Dow Jones Industrial Average.

NASDAQ

Log-return of NASDAQ.

Details

This data set has been utilized in the source below and can be downloaded from the web-site of the Journal of Applied Econometrics (see link below).

Source

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

References

http://qed.econ.queensu.ca/jae/2002-v17.5/van_der_weide/

See Also

BVDW

Examples

data(VDW)
str(VDW)

Autocorrelations of a Matrix Process

Description

This function computes the autocorrelation matrix for a given lag. For instance, it is used for estimating GO-GARCH models whence the method of moments is utilized.

Usage

cora(SSI, lag = 1, standardize = TRUE)

Arguments

Details

This function computes the autocorrelation matrix according to:

\hat{\Gamma}_k (s) = \frac{1}{n} \sum_{t = k + 1}^n S_t S_{t-k}

\hat{\Phi}_k (s) = \hat{\Gamma}_0 (s)^{-1/2} \hat{\Gamma}_k (s) \hat{\Gamma}_0 (s)^{-1/2}

It is computationally assured that \hat{\Phi}_k (s) is symmetric by setting it equal to: \hat{\Phi}_k (s) = \frac{1}{2}(\hat{\Phi}_k (s) + \hat{\Phi}_k (s)'). The standardization matrix \hat{\Gamma}_0 (s)^{-1/2} is derived from the singular value decomposition of the co-variance matrix at lag zero.

Value

Author(s)

Bernhard Pfaff

References

Boswijk, H. Peter and van der Weide, Roy (2009), Method of Moments Estimation of GO-GARCH Models, Working Paper, University of Amsterdam, Tinbergen Institute and World Bank.

See Also

gogarch

Methods for Function goest

Description

These are methods for estimating GO-GARCH models. Currently only a method for estimating GO-GARCH models by Maximum-Likelihood is implemented.

Details

The declared estimation methods are called from function gogarch.

Methods

goest

signature(object = "Goestica")

goest

signature(object = "Goestmm")

goest

signature(object = "Goestml")

goest

signature(object = "Goestnls")

Author(s)

Bernhard Pfaff

See Also

garchFit, Goestica, Goestml, Goestnls, Goestmm, gogarch

Specification and estimation of GO-GARCH models

Description

This function steers the specification and estimation of GO-GARCH models.

Usage

gogarch(data, formula, scale = FALSE, estby = c("ica", "mm", "ml", "nls"),
  lag.max = 1, initial = NULL, garchlist = list(init.rec = "mci", delta
  = 2, skew = 1, shape = 4, cond.dist = "norm", include.mean = FALSE,
  include.delta = NULL, include.skew = NULL, include.shape = NULL,
  leverage = NULL, trace = FALSE, algorithm = "nlminb", hessian =
  "ropt", control = list(), title = NULL, description = NULL), ...) 

Arguments

Details

The ellipsis argument is passed to the function fastICA if estby = "ica" has been set, or to optim if estby = "nls" is employed or to nlminb if the GO-GARCH model is estimated by maximum likelihood, i.e., estby = "ml". It is not employed if the methods of moments estimator is chosen.

If the argument initial is left NULL, the starting values are computed according seq(3.0, 0.1, length.out = l), whereby l is the length of initial for estby = "ml" and are set to rep(0.1, d, whereby for method = "nls". This length must be equal to m * (m - 1)/2 for estimation by Maximum-Likelihood and m * (m + 1)/2 for estimation by non-linear least-Squares, whereby m is the number of columns of data.

Value

Dependent on the chosen estimation method either an object of class Goestica or, Goestmm or Goestml or Goestnls is returned. All of these classes extend the GoGARCH class.

Author(s)

Bernhard Pfaff

References

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

Boswijk, H. Peter and van der Weide, Roy (2006), Wake me up before you GO-GARCH, Tinbergen Institute Discussion Paper, TI 2006-079/4, University of Amsterdam and Tinbergen Institute.

Boswijk, H. Peter and van der Weide, Roy (2009), Method of Moments Estimation of GO-GARCH Models, Working Paper, University of Amsterdam, Tinbergen Institute and World Bank.

Broda, S.A. and Paolella, M.S. (2008): CHICAGO: A Fast and Accurate Method for Portfolio Risk Calculation, Swiss Finance Institute, Research Paper Series No. 08-08, Zuerich.

See Also

GoGARCH, Goestica, Goestmm, Goestnls, Goestml, goest-methods

Examples

## Not run: 
library(vars)
## Boswijk / van der Weide (2009)
data(BVDWSTOXX)
BVDWSTOXX <- zoo(x = BVDWSTOXX[, -1], order.by = BVDWSTOXX[, 1])
BVDWSTOXX <- window(BVDWSTOXX, end = as.POSIXct("2007-12-31"))
BVDWSTOXX <- diff(log(BVDWSTOXX))
sectors <- BVDWSTOXX[, c("AutoParts", "Banks", "OilGas")]
sectors <- apply(sectors, 2, scale, scale = FALSE)
gogmm <- gogarch(sectors, formula = ~garch(1,1), estby = "mm",
         lag.max = 100)
gogmm
## Boswijk / van der Weide (2006)
data(BVDW)
BVDW <- zoo(x = BVDW[, -1], order.by = BVDW[, 1])
BVDW <- diff(log(BVDW)) * 100
gognls <- gogarch(BVDW, formula = ~garch(1,1), scale = TRUE,
          estby = "nls")
gognls
## van der Weide (2002)
data(VDW)
var1 <- VAR(scale(VDW), p = 1, type = "const")
resid <- residuals(var1)
gogml <- gogarch(resid, ~garch(1, 1), scale = TRUE,
         estby = "ml", control = list(iter.max = 1000))
gogml
solve(gogml@Z)

## End(Not run)

Constructor function for objects of class "Goinit"

Description

This function can be utilized to create objects of class Goinit. These objects are the starting point for estimating GO-GARCH models.

Usage

goinit(X, garchf = ~garch(1, 1), scale = FALSE)

Arguments

Details

This function computes the variance/covariance matrix of X. Next the singular value decomposition is applied and the projection matrix as well as the diagonal matrix with the square roots of the eigen values are computed.

Value

An object of class Goinit.

Author(s)

Bernhard Pfaff

See Also

Goinit

Examples

## Not run: 
library(vars)
data(VDW)
var1 <- VAR(VDW, p = 1, type = "const")
resid <- resid(var1)
goinit(resid, scale = TRUE)

## End(Not run)

Log-Likelihood function of GO-GARCH models

Description

This function returns the negative of the log-Likelihood function for GO-GARCH models.

Usage

gollh(params, object, garchlist)

Arguments

Details

The log-Likelihood function of GO-GARCH models is given as:

L_{\theta, \alpha, \beta} = - \frac{1}{2} \sum_{t=1}^T m \log(2\pi) + \log|Z_\theta Z_\theta '| + \log|H_t| + y' H_t^{-1}y_t

whereby Z = P \Delta^{\frac{1}{2}} U_0, y_t = Z^{-1}x_t and H_t is the conditional variance matrix of the independent components.

Value

Author(s)

Bernhard Pfaff

References

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

See Also

garchFit

Non-linear least-squares estimation of matrix B

Description

This is the target function for estimating the matrix B by non-linear least-squares. It is used in the estimation method goest if method = "nls" is chosen.

Usage

gonls(params, SSI)

Arguments

Details

Boswijk and van der Weiden (2006) proposed the following criterion function:

S(A) = \frac{1}{n} \sum_{t = 1}^n tr([s_t s_t' - I_m - B(s_{t-1} s_{t-1}' - I_m)B]^2) = S^*(B)

for retrieving the matrix U. This matrix is the eigen vector matrix of B. The linear map Z = P \Delta^{1/2} U and its inverse can then be computed for calculating the component matrix Y = X Z^{-1}.

Value

Author(s)

Bernhard Pfaff

References

Boswijk, H. Peter and van der Weide, Roy (2006), Wake me up before you GO-GARCH, Tinbergen Institute Discussion Paper, TI 2006-079/4, University of Amsterdam and Tinbergen Institute.

See Also

gogarch

Creates an object of class GoGARCH based on Euler angles

Description

This function returns an object of class GoGARCH based on an input vector of Euler angles.

Usage

gotheta(theta, object, garchlist = list(init.rec = "mci", delta = 2,
skew = 1, shape = 4, cond.dist = "norm", include.mean = FALSE,
include.delta = NULL, include.skew = NULL, include.shape = NULL,
leverage = NULL, trace = FALSE, algorithm = "nlminb", hessian = "ropt",
control = list(), title = NULL, description = NULL))

Arguments

Details

In a first step the orthogonal matrix U is computed as the product of rotation matrices given the vector theta of Euler angles with the function UprodR. The linear map Z is computed next as Z = P D^{\frac{1}{2}} U'. The unobserved components Y are calculated as Y = X Z^{-1}. These are then utilized in the estimation of the univariate GARCH models according to object@garchf. The conditional variance/covariance matrices are calculated according to V_t = Z H_t Z' whereby H_t signifies a matrix with the conditional variances of the unvariate GARCH models on its diagonal.

Value

Returns an object of class GoGARCH.

Author(s)

Bernhard Pfaff

References

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

See Also

Goinit, GoGARCH, Goestml, garchFit

Examples

## Not run: 
library(vars)
data(VDW)
var1 <- VAR(VDW, p = 1, type = "const")
resid <- resid(var1)
gin <- goinit(resid, scale = TRUE)
gotheta(0.5, gin)

## End(Not run)

Returns a symmetric matrix from a vector

Description

This function returns the symmetric matrix X from a vector that resulted from v = vech(X).

Usage

unvech(v)

Arguments

Details

The vector v must have length equal to m * (m + 1) / 2, whereby m is a dimension of the symmetric matrix X_{m \times m}.

Value

Author(s)

Bernhard Pfaff

See Also

vec

Examples

v <- c(1, 2, 3, 4, 5, 6)
unvech(v)

Validation function for objects of class Goinit

Description

This function validates objects of class Goinit.

Usage

validGoinitObject(object)

Arguments

Details

This function is utilized by validObject(). It is tested whether object@V, object@P, object@Dsqr are square matrices; object@V coincides with the singular value decomposition.

Value

Author(s)

Bernhard Pfaff

See Also

Goinit, goinit

Examples

data(VDW)
go <- goinit(VDW)
validObject(go)

Validation function for objects of class Orthom

Description

This function validates objects of class Orthom.

Usage

validOrthomObject(object)

Arguments

Details

This function is utilized by validObject(). It is tested whether object@M is a square matrix, has det(M) = 1 and MM' = I.

Value

Author(s)

Bernhard Pfaff

See Also

Orthom

Examples

theta <- c(pi/3, pi/5, pi/7)
U <- UprodR(theta)
validObject(U)