robustGarch (version 0.4.2)

robGarch: Robust GARCH(1,1) Model Estimation

Description

Computes "BM" robust Garch(1,1) model parameter estimate by using a bounded objective function and a bounded conditional variance recursion. Alternatively, it computes: (1) "M" estimates by using only the bounded objective function, (2) "QML" estimates based on a typically incorrect assumption of normally distributed innovations, (3) "t-MLE" estimates based on an assumption of an innovations t-distributed MLE with unknown location, scale,and degrees of freedom parameters. CHECK IF (3) IS CORRECT.

Usage

robGarch(
  data,
  fitMethod = c("BM", "M", "QML", "MLE"),
  robTunePars = c(0.8, 3),
  optChoice = c("Rsolnp", "nloptr", "nlminb"),
  initialPars = c(5e-04, 0.15, 0.75),
  SEmethod = c("numDeriv", "optim", "sandwich"),
  optControl = list(trace = 0)
)

Value

A list object of class “robustGarch” with components:

data

the input xts object

fitMethod

the the fitMethod specified

robtunePars

the robtunePars specified

initialPars

the initialPars specified

optChoice

the optChoice specified

coefEstimates

computed parameter estimates

sigma

conditional standard deviation xts class time series

SEmethod

the specidied of calculating standard errors

observedInfoMat

observed information matrix

optDetails

a list containing the optChoice specified, the control values specified, and the optChoice minimized objective, and convergence status message

Arguments

data

an xts object

fitMethod

character valued name of fitting method, one of "BM", "M" "QML" or "tMLE", with "BM" the default value.

robTunePars

a numeric vector c(cM,cFlt) that controls the extent of fitMethod robustness, with default c(0.8,3.0).

optChoice

character valued optChoice name, one of "Rsolnp", "nloptr", "nlminb", with default "Rsolnp".

initialPars

numeric user-defined initial parameters c(gamma0, alpha0, beta0) for use by optChoice, with default values c(0.0005, 0.15, 0.75).

SEmethod

character valued name of standard error method, one of "numDeriv", "optim", "sandwich", with default "numDeriv".

optControl

list of arguments passed to optChoice, with default list(trace=0).

Details

The "BM" fit method delivers the highest robustness by using a half-Huber psi function to bound the normal distribution log-likelihood, and using a Huber psi function to prevent the propagation of influential outliers in the variance recursion. The "M" method is obtained by dropping the BM bounding of the variance recursion, and is therefore less robust toward outliers.

ECHO OR DAN, PLEASE PROVIDE DETAILS FOR optControl. For details of the list of control arguments, please refer to nloptr::nloptr, Rsolnp::solnp, nlminb. The SEmethod default "numDeriv" is based on the Hessian from the optimization.

References

Muler, N. and Yohai, V. (2008). Robust estimates for GARCH models. Journal of Statistical Planning and Inference, 138, 2918-2940.

Examples

if (requireNamespace("PCRA", quietly = TRUE)) {
  ret <- PCRA::retOFG
  ret <- ret$RET
  (robFitBM <- robGarch(ret, fitMethod = "BM"))
  sum(robFitBM$fitted_pars[2:3])
  summary(robFitBM)
}