# egarch {egarch}

### Description

This function fits an Exponential Generalized Autoregressive Conditional Heteroscedastic Model (EGARCH(p, q)-Model) with normal or ged distributed innovations to a given univariate time series.

### Usage

egarch(x, order, include.shape = FALSE, include.mu = FALSE, control = list())

### Arguments

- x
- a time series.
- order
- integer vector with the p and q component of EGARCH(p, q). See Details for more information.
- include.shape
- logical flag. If
`include.shape = TRUE`

the shape parameter is assumed to be 2, otherwise it will be estimated during the optimization. - include.mu
- logical flag. If
`include.mu = TRUE`

the mean parameter will be estimated, otherwise it is assumed to be 0. - control
- list of control parameters, the same as declared in
`optim`

.

### Details

There are different definitions of the EGARCH model. The conditional variance process of the form + γ[q] (abs{Z[t-q]} - E(abs{Z[t-q]})) is used here. To calculate the maximum likelihood estimates `egarch`

uses the simplex algorithm of Nelder and Mead. For more details see Nelder and Mead (1965). The `optimi`

function used here is a slightly modified version of R Core Teams `optim`

function.

### Values

Returns a list of class "egarch" with the following elements: ...

- beta
- estimated beta coefficients of the fitted EGARCH model.
- eta
- estimated eta coefficients of the fitted EGARCH model.
- gamma
- estimated gamma coefficients of the fitted EGARCH model.
- nu
- estimated shape parameter of the fitted EGARCH model. This parameter is only estimated when
`include.shape = TRUE`

. - mu
- estimated mean of the fitted EGARCH model. This parameter is only estimated when when
`include.mu = TRUE`

. - ics
- values of the AIC-, BIC- and HQ-criterion for the fitted EGARCH model.

### References

Nelder J.A., Mead R. (1965): A simplex algorithm for function minimization. *Computer Journal* 7, 308 - 313.

Nelson D.B. (1991): Conditional Heteroskedasticity in Asset Returns: A New Approach. *Econometrica* 59, 347 - 370.

Nocedal J., Wright S.J. (1999): *Numerical Optimization*. Springer.

Straumann D. (2005): *Estimation in Conditionally Heteroscedastic Time Series Models*. Springer.

Wuertz D., Chalabi Y., Luksan L.: Parameter Estimation of ARMA models with GARCH/APARCH errors. *Journal of Statistical Software*.

### Examples

# Simulating and fitting of an EGARCH(1,1) model with no mean and normal # distributed innovations x <- egarchSim(mu = 0, beta = c(0.01, 0.8), eta = -0.5, gamma = 0.4, nu = 2, n = 2000) fit <- egarch(x = x, order = c(1, 1)) # Simulating and fitting of an EGARCH(2,2) model with no mean and ged # distributed innovations x <- egarchSim(mu = 0, beta = c(0.01, 0.2, 0.5), eta = c(-0.3, -0.2), gamma = c(0.3, 0.4), nu = 1.5, n = 2000) fit <- egarch(x = x, order = c(2, 2), include.shape = TRUE) # Simulating and fitting of an EGARCH(2,1) model with mean = 0.2 and # normal distributed innovations x <- egarchSim(mu = 0.2, beta = c(0.01, 0.3, 0.6), eta = -0.4, gamma = 0.6, nu = 2, n = 5000) fit <- egarch(x = x, order = c(2, 1), include.mu = TRUE)

Documentation reproduced from package egarch, version 1.0.0. License: GPL (>= 2)