Package 'mgarchBEKK'

Estimate MGARCH-BEKK processes

Description

Provides the MGARCH-BEKK estimation procedure.

Usage

BEKK(
  eps,
  order = c(1, 1),
  params = NULL,
  fixed = NULL,
  method = "BFGS",
  verbose = F
)

Arguments

eps	Data frame holding time series.
order	BEKK(p, q) order. An integer vector of length 2 giving the orders of the model to be fitted. order[2] refers to the ARCH order and order[1] to the GARCH order.
params	Initial parameters for the optim function.
fixed	Vector of parameters to be fixed.
method	The method that will be used by the optim function.
verbose	Indicates if we need verbose output during the estimation.

Details

BEKK estimates a BEKK(p,q) model, where p stands for the GARCH order, and q stands for the ARCH order.

Value

Estimation results packaged as BEKK class instance.

eps

a data frame contaning all time series

length

length of the series

order

order of the BEKK model fitted

estimation.time

time to complete the estimation process

total.time

time to complete the whole routine within the mvBEKK.est process

estimation

estimation object returned from the optimization process, using optim

aic

the AIC value of the fitted model

est.params

list of estimated parameter matrices

asy.se.coef

list of asymptotic theory estimates of standard errors of estimated parameters

cor

list of estimated conditional correlation series

sd

list of estimated conditional standard deviation series

H.estimated

list of estimated series of covariance matrices

eigenvalues

estimated eigenvalues for sum of Kronecker products

uncond.cov.matrix

estimated unconditional covariance matrix

residuals

list of estimated series of residuals

References

Bauwens L., S. Laurent, J.V.K. Rombouts, Multivariate GARCH models: A survey, April, 2003

Bollerslev T., Modelling the coherence in short-run nominal exchange rate: A multivariate generalized ARCH approach, Review of Economics and Statistics, 498–505, 72, 1990

Engle R.F., K.F. Kroner, Multivariate simultaneous generalized ARCH, Econometric Theory, 122-150, 1995

Engle R.F., Dynamic conditional correlation: A new simple class of multivariate GARCH models, Journal of Business and Economic Statistics, 339–350, 20, 2002

Tse Y.K., A.K.C. Tsui, A multivariate generalized autoregressive conditional heteroscedasticity model with time-varying correlations, Journal of Business and Economic Statistics, 351-362, 20, 2002

Examples

## Simulate series:
simulated <- simulateBEKK(2, 1000, c(1,1))

## Prepare the matrix:
simulated <- do.call(cbind, simulated$eps)

## Estimate with default arguments:
estimated <- BEKK(simulated)

## Not run: 
## Show diagnostics:
diagnoseBEKK(estimated)

## End(Not run)

---

Diagnose BEKK process estimation

Description

Provides diagnostics for a BEKK process estimation.

Usage

diagnoseBEKK(estimation)

Arguments

estimation

The return value of the mvBEKK.est function

Details

This procedure provides console output and browsable plots for a given BEKK process estimation. Therefore, it is meant to be interactive as the user needs to proceed by pressing c on the keyboard to see each plot one-by-one.

Value

Nothing special

Examples

## Simulate series:
simulated = simulateBEKK(2, 1000, c(1,1))

## Prepare the matrix:
simulated = do.call(cbind, simulated$eps)

## Estimate with default arguments:
estimated = BEKK(simulated)

## Not run: 
## Show diagnostics:
diagnoseBEKK(estimated)

## End(Not run)

---

Bivariate GJR Estimation

Description

Provides bivariate GJR (mGJR(p,q,g)) estimation procedure.

Usage

mGJR(
  eps1,
  eps2,
  order = c(1, 1, 1),
  params = NULL,
  fixed = NULL,
  method = "BFGS"
)

Arguments

eps1	First time series.
eps2	Second time series.
order	mGJR(p, q, g) order a three element integer vector giving the order of the model to be fitted. order[2] refers to the ARCH order and order[1] to the GARCH order and order[3] to the GJR order.
params	Initial parameters for the optim function.
fixed	A two dimensional vector that contains the user specified fixed parameter values.
method	The method that will be used by the optim function. See ?optim for available options.

Value

Estimation results packaged as mGJR class instance. The values are defined as:

eps1

first time series

eps2

second time series

length

length of each series

order

order of the mGJR model fitted

estimation.time

time to complete the estimation process

total.time

time to complete the whole routine within the mGJR.est process

estimation

estimation object returned from the optimization process, using optim

aic

the AIC value of the fitted model

est.params

estimated parameter matrices

asy.se.coef

asymptotic theory estimates of standard errors of estimated parameters

cor

estimated conditional correlation series

sd1

first estimated conditional standard deviation series

sd2

second estimated conditional standard deviation series

H.estimated

estimated series of covariance matrices

eigenvalues

estimated eigenvalues for sum of Kronecker products

uncond.cov.matrix

estimated unconditional covariance matrix

resid1

first estimated series of residuals

resid2

second estimated series of residuals

References

Bauwens L., S. Laurent, J.V.K. Rombouts, Multivariate GARCH models: A survey, April, 2003

Bollerslev T., Modelling the coherence in short-run nominal exchange rate: A multivariate generalized ARCH approach, Review of Economics and Statistics, 498–505, 72, 1990

Engle R.F., K.F. Kroner, Multivariate simultaneous generalized ARCH, Econometric Theory, 122-150, 1995

Engle R.F., Dynamic conditional correlation: A new simple class of multivariate GARCH models, Journal of Business and Economic Statistics, 339–350, 20, 2002

Tse Y.K., A.K.C. Tsui, A multivariate generalized autoregressive conditional heteroscedasticity model with time-varying correlations, Journal of Business and Economic Statistics, 351-362, 20, 2002

Examples

## Not run: 
  sim = BEKK.sim(1000)
  est = mGJR(sim$eps1, sim$eps2)

## End(Not run)

---

Simulate BEKK processes

Description

Provides a procedure to simulate BEKK processes.

Usage

simulateBEKK(series.count, T, order = c(1, 1), params = NULL)

Arguments

series.count	The number of series to be simulated.
T	The length of series to be simulated.
order	BEKK(p, q) order. An integer vector of length 2 giving the orders of the model to fit. order[2] refers to the ARCH order and order[1] to the GARCH order.
params	A vector containing a sequence of parameter matrices' values.

Details

simulateBEKK simulates an N dimensional BEKK(p,q) model for the given length, order list, and initial parameter list where N is also specified by the user.

Value

Simulated series and auxiliary information packaged as a simulateBEKK class instance. Values are:

length

length of the series simulated

order

order of the BEKK model

params

a vector of the selected parameters

true.params

list of parameters in matrix form

eigenvalues

computed eigenvalues for sum of Kronecker products

uncond.cov.matrix

unconditional covariance matrix of the process

white.noise

white noise series used for simulating the process

eps

a list of simulated series

cor

list of series of conditional correlations

sd

list of series of conditional standard deviations

References

Bauwens L., S. Laurent, J.V.K. Rombouts, Multivariate GARCH models: A survey, April, 2003

Bollerslev T., Modelling the coherence in short-run nominal exchange rate: A multivariate generalized ARCH approach, Review of Economics and Statistics, 498–505, 72, 1990

Engle R.F., K.F. Kroner, Multivariate simultaneous generalized ARCH, Econometric Theory, 122-150, 1995

Engle R.F., Dynamic conditional correlation: A new simple class of multivariate GARCH models, Journal of Business and Economic Statistics, 339–350, 20, 2002

Tse Y.K., A.K.C. Tsui, A multivariate generalized autoregressive conditional heteroscedasticity model with time-varying correlations, Journal of Business and Economic Statistics, 351-362, 20, 2002

Examples

## Simulate series:
simulated = simulateBEKK(2, 1000, c(1,1))

---