ARfilter: Robust Fitting of Autoregressive Models by Robust Filtering

In robts: Robust Time Series Analysis

Description

Robustly fits AR models using a robust filter algorithm. See Dürre et al. (2015) for details.

This is a workhorse function which is called by several other functions in this package.

Usage

ARfilter(x, order.max, aicpenalty = function(p) {2*p}, psi.l = 2, psi.0 = 3)

Arguments

x	univariate numeric vector or time series object.
order.max	integer value determining the maximum order of the AR fit.
psi.l	numeric value determining the psi function used for filtering, see link{smoothpsi}. For absolute values lower than psi.l the psi function is linear.
psi.0	numeric value determining the psi function used for filtering, see link{smoothpsi}. For absolute values larger than psi.0 the psi function is zero.
aicpenalty	function of the model order, indicating the penalty for a larger model. See Details.

Details

The function fits AR models of increasing order by a robust version of the Durbin Levinson algorithm as described in Chapter 8 of Maronna et al. (2006). The AR coefficients are estimated by minimizing a robust scale (scaleTau2) of one step ahead residuals of robustly filtered predictors. The filter process basically compares the predicted value under the estimated model with the observed one and transforms the corresponding residual with the psi function. The transformed value is then set to the sum of the predicted value and the transformed residual. For more details see Maronna et al. (2006) and Dürre et al. (2015).

Following Maronna et al. (2006), the psi function should fulfill two properties. It should be the identity for small absolute values and zero for large absolute values. Both thresholds can be determined by psi.l and psi.0. Here the psi function is chosen to be two times continuously differentiable, see link{smoothpsi} and Dürre et al. (2015) for a formal definition.

Value

List containing the following values:

pacf	numeric vector representing the successively estimated partial correlations of the model at lags 1,...,p.
var	numeric vector containing the estimations of the residual scale for AR models of order 0,...,p.
acf	numeric vector of estimated autocorrelations of a model of order order.max at lags 1,...,p.
aic	numeric vector of AIC values of AR models of order 0,...,p.
filtered	numeric matrix containing the robustly filtered time series of AR models of different orders. The first column corresponds to the AR(0) model, the second to the AR(1) model and so on.
ar	list containing the estimated AR coefficients of AR models of different orders. The first list element corresponds to the AR(0) model, the second to the AR(1) model and so on.

Author(s)

Alexander Dürre, Tobias Liboschik and Jonathan Rathjens

References

Dürre, A., Fried, R. and Liboschik, T. (2015): Robust estimation of (partial) autocorrelation, Wiley Interdisciplinary Reviews: Computational Statistics, vol. 7, 205–222, doi: wics.1351.

Maronna, R., Martin, D. and Yohai, V. (2006): Robust statistics, Wiley, Chichester, doi: 10.1002/0470010940.

See Also

arrob.filter for robust fitting of AR models and acfrob.filter for robust estimation of the autocorrelation function, both based on robust filtering. filterrob for robust filtering of time series.

Examples

set.seed(1066)
tss <- arima.sim(model = list(ar = 0.3, ma = 0.5), n = 100)
ARfilter(tss, order.max = 5)

robts documentation built on May 2, 2019, 4:55 p.m.