internalarGM: Internal functions of package robKalman - psi functions
In robKalman: Robust Kalman Filtering

Description Usage Arguments Details Value Author(s) See Also

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

.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, ...)

`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

to be filled

.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.