GM-estimates for AR parameters

Share:

Description

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

Usage

1
2
3
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 bernhard.spangl@boku.ac.at,

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