robustGARCH-robGarch: Robust GARCH(1,1) Model Estimation

In EchoRLiu/robustGarch: Robust Garch(1,1) Model

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)
)

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.

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

References

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

Examples

data("gspc")
fit <- robGarch(gspc[1:604], fitMethod = "BM")
summary(fit)

EchoRLiu/robustGarch documentation built on Jan. 7, 2025, 11:19 p.m.