# BEKK: Estimate MGARCH-BEKK processes In mgarchBEKK: Simulating, Estimating and Diagnosing MGARCH (BEKK and mGJR) Processes

 BEKK R Documentation

## 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` refers to the ARCH order and `order` 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)

```

mgarchBEKK documentation built on Dec. 6, 2022, 9:10 a.m.