wle (version 0.9-91)

wle.aic.ar: Weighted Akaike Information Criterion for AR models

Description

The function evaluate the Weighted Akaike Information Criterion for AutoRegressive Models. This is a robust model selection method to choose the order of an AutoRegressive model.

Usage

wle.aic.ar(x, order = c(1, 0), seasonal = list(order = c(0, 0), period =NA), group, group.start, group.step = group.start, xreg = NULL, include.mean = TRUE, na.action = na.fail, tol = 10^(-6), tol.step = tol, equal = 10^(-3), equal.step = equal, raf = "HD", var.full = 0, smooth = 0.0031, smooth.ao = smooth, boot = 10, boot.start = 10, boot.step = boot.start, num.sol = 1, x.init = 0, x.seasonal.init = 0, max.iter.out = 20, max.iter.in = 50, max.iter.start = 200, max.iter.step = 500, verbose = FALSE, w.level = 0.4, min.weights = 0.5, population.size = 10, population.choose = 5, elements.random = 2, wle.start = FALSE, init.values = NULL, num.max = NULL, num.sol.step = 2, min.weights.aic = 0.5, approx.w = TRUE, ask = TRUE, alpha = 2, method = "WLS")

Arguments

x

a univariate time series.

order

maximum order to investigate. A specification of the non-seasonal part of the ARI model: the two components (p,d) are the AR order and the degree of differencing.

seasonal

a specification of the seasonal part of the ARI model, plus the period (which defaults to frequency(x)).

group

the dimension of the bootstap subsamples.

group.start

the dimension of the bootstap subsamples used in the starting process if wle.init=TRUE.

group.step

the dimension of the bootstap subsamples used in a step, it must be less than group.

xreg

optionally, a vector or matrix of external regressors, which must have the same number of rows as x.

include.mean

Should the ARI model include a mean term? The default is TRUE for undifferenced series, FALSE for differenced ones (where a mean would not affect the fit nor predictions).

na.action

function to be applied to remove missing values.

tol

the absolute accuracy to be used to achieve convergence of the algorithm.

tol.step

the absolute accuracy to be used to achieve convergence in a step.

equal

the absolute value for which two roots are considered the same. (This parameter must be greater than tol).

equal.step

the absolute value for which two roots are considered the same in a step. (This parameter must be greater than tol.step).

raf

type of Residual adjustment function to be use: raf="HD": Hellinger Distance RAF, raf="NED": Negative Exponential Disparity RAF, raf="SCHI2": Symmetric Chi-Squared Disparity RAF.

var.full

An estimate of the residual variance for the full model.

smooth

the value of the smoothing parameter.

smooth.ao

the value of the smoothing parameter used in the outliers classificaton, default equal to smooth.

boot

the number of starting points based on boostrap subsamples to use in the search of the roots.

boot.start

the number of starting points based on boostrap subsamples to use in the search of the roots in the starting process.

boot.step

the number of starting points based on boostrap subsamples to use in the search of the roots in a step.

num.sol

maximum number of roots to be searched.

x.init

initial values, a vector with the same length of the AR order, or a number, default is 0.

x.seasonal.init

initial values, a vector with the same length of the SAR order, or a number, default is 0.

max.iter.out

maximum number of iterations in the outer loop.

max.iter.in

maximum number of iterations in the inner loop.

max.iter.start

maximum number of iterations in the starting process.

max.iter.step

maximum number of iterations in a step.

verbose

if TRUE warnings are printed.

w.level

the threshold used to decide if an observation could be an additive outlier.

min.weights

see details.

population.size

see details.

population.choose

see details.

elements.random

see details.

wle.start

if TRUE a weighted likelihood estimation is used to have a starting value.

init.values

a vector with initial values for the AR and seasonal AR coefficients and the innovations variance.

num.max

maximum number of observations can be considered as possible additive outliers.

num.sol.step

maximum number of roots to be searched in a step.

min.weights.aic

see details.

approx.w

logical: if TRUE an approximation is used to evaluate the weights in the outlier identification procedure.

ask

logical. If TRUE, in the case of multiple roots in the full model, the users is asked for selecting the root.

alpha

penalty value.

method

if "WLE" the parameters are estimated using weighted likelihood estimating equations in the reduced models, otherwise if "WLS" a weighted least squares approach is used with weights based on the full model.

Value

A list of class wle.aic.ar with the following components:

full.model

the results for the full model, that is an object of class wle.arima see wle.ar help for further details.

waic

Weighted Akaike Information Criterion for each submodels.

call

match.call result.

Details

min.weights: the weighted likelihood equation could have more than one solution. These roots appear for particular situation depending on contamination level and type. We introduce the min.weight parameter in order to choose only between roots that do not down weight everything. This is not still the optimal solution, and perhaps, in the new release, this part will be change.

min.weights.aic is used as min.weights but in the full model. The algorithm used to classify the observations as additive outliers is made by a genetic algorithm. The population.size, population.choose and elements.random are parameters related to this algorithm.

The function wle.ar.wls is used to estimate the parameter of an autoregressive model by weighted least squares where the weights are those from the weighted likelihood estimating equation of the full model (the model with the hightest order).

References

Agostinelli C, (2004) Robust Akaike Information Criterion for ARMA models, Rendiconti per gli Studi Economici Quantitativi, 1-14, isbn: 88-88037-10-1.

Agostinelli C., (2003) Robust time series estimation via weighted likelihood, in: Development in Robust Statistics. International Conference on Robust Statistics 2001, Eds. Dutter, R. and Filzmoser, P. and Rousseeuw, P. and Gather, U., Physica Verlag.

See Also

wle.ar

Examples

data(rocky)

res <- wle.aic.ar(x=rocky, order=c(6,0), group=50, group.start=30, method="WLS")
res
plot(res$full.model$weights)