Internal functions of package robKalman — psi functions

Description

These functions are used internally by package robKalman for the ACM filter — ψ-functions

Usage

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.ARmodel(x, p)
.invCp(p, s, Phi)
.Weights(p, Z, invCp, type, psi2, c)
.startval(y, Z, tol)
.BH(k=1.345) 
.BB(c=4.685)
.weights(r, s, u, v, psi1, ...)
.IWLS(y, Z, phi.ini, s.ini, u, v, psi1, niter, tol, ...)

Arguments

x

univarite time series (vector)

p

order of AR(p) process

s

vector of sx and innovation scale estimates for AR(p-1) models of order 1 to (p-1)

Phi

(p-1)x(p-1) matrix of AR(p-1) model parameters

Z

AR(p) model matrix

invCp

matrix from function .invCp to compute metric

type

type of GM-estimates — character: currently: "Mallows" or "Schweppe"

psi1, psi2

type of ψ function; current possibilities: "Huber", "Tukey", "Hampel", "Ident"

c, k

tuning constants

y

response vector of AR(p) model

tol

tolerance level

r

residuals

s

innovations scale parameter

u, v

weights

...

additional arguments (tuning constants) for influence functions

phi.ini

initial AR(p) model parameters

s.ini

initial innovations scale parameter

niter

maximal number of iterations

Details

to be filled

Value

.ARmodel(x, p) returns design matrix Z and response vector y of an AR(p) model (as list with corresponding elements).
.invCp(p, s, Phi) computes the inverse p x p covariance matrix.
.Weights computes weights for Mallows- or Schweppe-type GM-estimates; returns a list with elements u, v.
.startval computes appropriate starting values; returns a list with elements phi, s.
.BH computes appropriate constant to obtain a consistent estimate for σ when using Huber's ψ function.
.BB computes appropriate constant to obtain a consistent estimate for σ when using Tukey's ψ function.
.weights computes appropriate weights for reweighting — returns a vector.
.IWLS iteratively reweighted least squares algorithm; returns a list with elements phi, s, w, B, niter.

Author(s)

Bernhard Spangl bernhard.spangl@boku.ac.at,

See Also

internalpsi