betategarch (version 3.3)

predict.tegarch: Generate volatility forecasts n-steps ahead

Description

Generates volatility forecasts from a model fitted by tegarch (i.e. a Beta-Skew-t-EGARCH model)

Usage

"predict"(object, n.ahead = 1, initial.values = NULL, n.sim = 10000, verbose = FALSE, ...)

Arguments

object

an object of class 'tegarch'.

n.ahead

the number of steps ahead for which prediction is required.

initial.values

a vector containing the initial values of lambda and lambdadagger (lambda1dagger and lambda2dagger for 2-component models). If NULL (default) then the fitted values associated with the last return-observation are used

n.sim

number of simulated skew t variates.

verbose

logical. If FALSE (default) then only the conditional standard deviations are returned. If TRUE then also the scale is returned.

...

additional arguments

Value

A zoo object. If verbose = FALSE, then the zoo object is a vector with the forecasted conditional standard deviations. If verbose = TRUE, then the zoo object is a matrix with forecasts of both the conditional scale and the conditional standard deviation

Details

The forecast formulas of exponential ARCH models are much more complicated than those of ordinary or non-exponential ARCH models. This is particularly the case when the conditional density is skewed. The forecast formula of the conditional scale of the Beta-Skew-t-EGARCH model is not available in closed form. Accordingly, some terms (expectations involving the skewed t) are estimated numerically by means of simulation.

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

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

tegarch, predict

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)

#plot forecasts of volatility 1-step ahead up to 10-steps ahead:
plot(predict(mymod, n.ahead=10))