tegarch {betategarch}

Estimate first order Beta-Skew-t-EGARCH models

Description

Fits a first order Beta-Skew-t-EGARCH model to a univariate time-series by exact Maximum Likelihood (ML) estimation. Estimation is via the nlminb function

Usage

tegarch(y, asym = TRUE, skew = TRUE, components = 1, initial.values = NULL,
  lower = NULL, upper = NULL, hessian = TRUE, lambda.initial = NULL,
  c.code = TRUE, logl.penalty = NULL, aux = NULL, ...)

Arguments

y

numeric vector, typically a financial return series.

asym

logical. TRUE (default) includes leverage or volatility asymmetry in the log-scale specification

skew

logical. TRUE (default) enables and estimates the skewness in conditional density (epsilon). The skewness method is that of Fernandez and Steel (1998)

components

Numeric value, either 1 (default) or 2. The former estimates a 1-component model, the latter a 2-component model

initial.values

NULL (default) or a vector with the initial values. If NULL, then the values are automatically chosen according to model (with or without skewness, 1 or 2 components, etc.)

lower

NULL (default) or a vector with the lower bounds of the parameter space. If NULL, then the values are automatically chosen

upper

NULL (default) or a vector with the upper bounds of the parameter space. If NULL, then the values are automatically chosen

hessian

logical. If TRUE (default) then the Hessian is computed numerically via the optimHess function. Setting hessian=FALSE speeds up estimation, which might be particularly useful in simulation. However, it also slows down the extraction of the variance-covariance matrix by means of the vcov method.

lambda.initial

NULL (default) or a vector with the initial value(s) of the recursion for lambda and lambdadagger. If NULL then the values are chosen automatically

c.code

logical. TRUE (default) is faster since it makes use of compiled C-code

logl.penalty

NULL (default) or a numeric value. If NULL then the log-likelihood value associated with the initial values is used. Sometimes estimation can result in NA and/or +/-Inf values, which are fatal for simulations. The value logl.penalty is the value returned by the log-likelihood function in the presence of NA or +/-Inf values

aux

NULL (default) or a list, se code. Useful for simulations (speeds them up)

...

further arguments passed to the nlminb function

Value

Returns a list of class 'tegarch' with the following elements:

y

the series used for estimation.

date

date and time of estimation.

initial.values

initial values used in estimation.

lower

lower bounds used in estimation.

upper

upper bounds used in estimation.

lambda.initial

initial values of lambda provided by the user, if any.

model

type of model estimated.

hessian

the numerically estimated Hessian.

sic

the value of the Schwarz (1978) information criterion.

par

parameter estimates.

objective

value of the log-likelihood at the maximum.

convergence

an integer code. 0 indicates successful convergence, see the documentation of nlminb.

iterations

number of iterations, see the documentation of nlminb.

evaluations

number of evaluations of the objective and gradient functions, see the documentation of nlminb.

message

a character string giving any additional information returned by the optimizer, or NULL. For details, see PORT documentation and the nlminb documentation.

NOTE

an additional message returned if one tries to estimate a 2-component model without leverage.

Note

Empty

Author(s)

Genaro Sucarrat, http://www.sucarrat.net/

References

Fernandez and Steel (1998), 'On Bayesian Modeling of Fat Tails and Skewness', Journal of the American Statistical Association 93, pp. 359-371.

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

Harvey and Sucarrat (2014), 'EGARCH models with fat tails, skewness and leverage'. Computational Statistics and Data Analysis 76, pp. 320-338.

Schwarz (1978), 'Estimating the Dimension of a Model', The Annals of Statistics 6, pp. 461-464.

Sucarrat (2013), 'betategarch: Simulation, Estimation and Forecasting of First-Order Beta-Skew-t-EGARCH models'. The R Journal (Volume 5/2), pp. 137-147.

See Also

tegarchSim, coef.tegarch, fitted.tegarch, logLik.tegarch, predict.tegarch, print.tegarch, residuals.tegarch, summary.tegarch, vcov.tegarch

Examples

##simulate series with 500 observations:
set.seed(123)
y <- tegarchSim(500, omega=0.01, phi1=0.9, kappa1=0.1, kappastar=0.05,
  df=10, skew=0.8)

##estimate a 1st. order Beta-t-EGARCH model and store the output in mymod:
mymod <- tegarch(y)

#print estimates and standard errors:
print(mymod)

#graph of fitted volatility (conditional standard deviation):
plot(fitted(mymod))

#graph of fitted volatility and more:
plot(fitted(mymod, verbose=TRUE))

#plot forecasts of volatility 1-step ahead up to 20-steps ahead:
plot(predict(mymod, n.ahead=20))

#full variance-covariance matrix:
vcov(mymod)