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egarch {egarch}

Fitting EGARCH models to Time Series
Package: 
egarch
Version: 
1.0.0

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)

Author(s)

Kerstin Konnerth,
R Core Team, the main parts of optimi.

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