wle.ar: Fit Autoregressive Models to Time Series - Preliminary...
In wle: Weighted Likelihood Estimation

Description Usage Arguments Details Value Author(s) References Examples

This is a preliminary version of functions for the estimation of the autoregressive parameters via Weighted Likelihood Estimating Equations and a cassification algorithm. The main function is wle.ar, the remain functions are for internal use and they should not call by the users. They are not documented here.

wle.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", 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, approx.w=TRUE)

`x`	a univariate time series.
`order`	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.
`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.
`num.sol.step`	maximum number of roots to be searched in a step.
`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.
`w.level`	the threshold used to decide if an observation could be an additive outlier.
`population.size`	see details.
`population.choose`	see details.
`elements.random`	see details.
`num.max`	maximum number of observations can be considered as possible additive outliers.
`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.
`verbose`	if `TRUE` warnings are printed.
`min.weights`	see details.
`approx.w`	logical: if `TRUE` an approximation is used to evaluate the weights in the outlier identification procedure.

min.weight: 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.

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.

`coef`	a vector of AR and regression coefficients.
`sigma2.coef`	the estimated variance matrix of the coefficients coef.
`sigma2`	the WLE of the innovations variance.
`arma`	a compact form of the specification, as a vector giving the number of AR, MA=0, seasonal AR and seasonal MA=0 coefficients, plus the period and the number of non-seasonal and seasonal differences.
`resid`	the residuals.
`resid.with.ao`	the residuals with the additive outliers effects.
`resid.without.ao`	the residuals without the additive outliers effects.
`x.ao`	the time series without the additive outliers effects.
`call`	the matched call.
`series`	the name of the series `x`.
`weights`	the weights.
`weights.with.ao`	the weights with the additive outliers effects.
`weights.without.ao`	the weights without the additive outliers effects
`tot.sol`	the number of solutions found.
`not.conv`	the number of starting points that does not converge after the `max.iter.out` iteration are reached.
`ao.position`	the position of the additive outliers.

Claudio Agostinelli

Agostinelli C., (2001) Robust time series estimation via weighted likelihood: some preliminary results, Working Paper n. 2001.3 Department of Statistics, University of Padova.

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.