arGM: GM-estimates for AR parameters

In robKalman: Robust Kalman Filtering

Description

This function realizes Martin's GM-estimates for AR parameters.

Usage

arGM(x, order=1, chr=1.5, iterh=maxiter, cbr=5.0, iterb=maxiter, 
     psi2="Tukey", c=4.0, type="Mallows", k=1.5, maxiter=100, 
     tol=1e-08, equal.LS=FALSE, ...) 

Arguments

x	univarite time series (vector)
order	order of AR(p) process
chr	tuning constant for Huber's ψ function
iterh	number of iterations for IWLS-alogrithm using Huber's ψ function
cbr	tuning constant for Tukey's ψ function
iterb	number of iterations for IWLS-alogrithm using Tukey's ψ function
psi2	influence function to determine the 'size of z_i', either "Ident", "Huber" or "Tukey"
c	tuning constant for psi2
type	type of GM-estimates, either "Mallows" or "Schweppe"
k	tuning constant for centering
maxiter	maximal number of iteration
tol	tolerance level
equal.LS	logical, for testing purpose only
...	further parameters to be passed to the functions HuberM or hubers

Details

to be filled

Value

a list with elements

ar	parameter estimate
sinnov	scale estimate for the innovations from AR(p) fits of orders 1 through p
Cx	an estimate of the p x p autocovariance matrix
mu	location estimate of x
sx	Huber scale estimate
u,v	weights for Mallows- or Schweppe-type GM-estimates
w	weights from IWLS algorithm
BH	consistency constant for σ when using Huber's ψ function
BB	consistency constant for σ when using Tukey's ψ function
niterh	number of iterations for IWLS-alogrithm using Huber's ψ function
niterb	number of iterations for IWLS-alogrithm using Tukey's ψ function
niter.testing	for testing purposes only

Author(s)

Bernhard Spangl [e-mail],

References

Martin, R.D. and Zeh, J.E. (1978): Generalized M-estimates for Autoregression Including Small-sample Efficiency Robustness
Martin, R.D. (1980): Robust Estimation of Autoregressive Models.
Martin, R.D. and Thomson, D.J. (1982): Robust-resistent Spectrum Estimation.
Stockinger, N. and Dutter, R. (1987): Robust Time Series Analysis: A Survey.

See Also

internalarGM, internalpsi

robKalman documentation built on May 2, 2019, 4:50 p.m.