tegarch.est: Estimates a first order Beta-skew-t-EGARCH model

Description

Provides Maximum Likelihood (ML) estimation of a first order Beta-skew-t-EGARCH model and computes, optionally, the Hessian. Estimation is via the nlminb function. EGARCH is short for Exponential Generalised Autoregressive Heteroscedasticity, a label that is often associated with Nelson's (1991) model. A shortcoming with Nelson's model is that the unconditional moments do not exist in general when the conditional density is t distributed. This is the major motivation behind Andrew Harvey's Beta-t-EGARCH class of models, which is an exponential GARCH model with leverage and t distributed conditional errors (possibly skewed).

Usage

tegarch.est(y, asym = TRUE, skew = TRUE, components = 1, initial.values = NULL,
  lower = NULL, upper = NULL, compute.hessian = FALSE, lambda.initial = NULL,
  c.code = TRUE, logl.penalty = -1e+100, verbose = TRUE, aux = NULL, ...)

Arguments

numeric vector, typically a financial return series.

asym

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

skew

logical, TRUE (default) or FALSE. TRUE 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 one-component model, the latter a two-component model.

initial.values

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

lower

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

upper

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

compute.hessian

logical, TRUE or FALSE (default). If TRUE then the Hessian is computed numerically using the optimHess function.

lambda.initial

NULL (default) or initial value(s) of the recursion for lambda or log-volatility. If NULL then the values are chosen automatically.

c.code

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

logl.penalty

NULL (default) or a numeric value. If NULL then the function chooses the value automatically. Sometimes estimation can result in NA or +/-Inf values, which can be fatal for simulations. The value logl.penalty is the value returned by the log-likelihood fu

verbose

logical, TRUE (default) or FALSE. FALSE provides faster estimation, because less results-output is generated.

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 with the following elements:
datedate and time of estimation.
initial.valuesinitial values used in estimation.
lowerlower bounds used in estimation.
upperupper bounds used in estimation.
modeltype of model estimated.
hessian.numericalHessian, numerically estimated.
parparameter estimates.
objectivevalue of the log-likelihood at the maximum.
convergenceAn integer code. 0 indicates successful convergence, see the documentation of nlminb.
iterationsNumber of iterations, see the documentation of nlminb.
evaluationsNumber of evaluations of the objective and gradient functions, see the documentation of nlminb.
messageA character string giving any additional information returned by the optimizer, or NULL. For details, see PORT documentation and the nlminb documentation.

References

Fernandez and Steel (1998), 'On Bayesian Modeling of Fat Tails and Skewness', Journal of the American Statistical Association 93, pp. 359-371. Harvey and Chakravarty (2008), 'Beta-t-(E)GARCH', Cambridge Working Papers in Economics 0840, Faculty of Economics, University of Cambridge. Nelson, Daniel B. (1991): 'Conditional Heteroskedasticity in Asset Returns: A New Approach', Econometrica 59, pp. 347-370. Harvey and Sucarrat (2012), 'EGARCH models with fat tails, skewness and leverage', Cambridge Working Papers in Economics 1236, Faculty of Economics, University of Cambridge.

Examples

Run this code

##simulate series with 500 observations:
set.seed(123)
y <- tegarch.sim(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.est(y)

##estimate the same model but with Hessian:
tegarch.est(y, compute.hessian=TRUE)