acfrob.RA: Robust Autocorrelation Estimation Based on Residual...

Description Usage Arguments Details Value Author(s) References See Also Examples

Description

Robustly estimates the autocorrelation function of a time series based on a robustly transformed time series. See Dürre et al. (2015) for details.

This function is intended for internal usage only. Users should rather use the wrapper function acfrob with argument approach = "acfRA".

Usage

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acfrob.RA(x, lag.max, psi = c("huber", "bisquare"), k, locfn = median, scalefn = mad,
      biascorr = TRUE, ...)

Arguments

x

univariate numeric vector or time series object.

lag.max

integer value giving the maximum lag at which to calculate the acf.

psi

character string indicating the psi function to be used. Must be either 'huber' for Huber's function or 'bisquare' for Tukey's function, see Details.

k

numeric tuning parameter determining the psi function. If missing, the function chooses k = 1.37 (for Huber's function) or k = 4.68 (for Tukey's function).

locfn

function which calculates a location estimator. Its argument must be a vector of the data.

scalefn

function which calculates a scale estimator. Its argument must be a vector of the data. One could for example use one of the functions Qn (the default), Sn, scaleTau2 (all from the package robustbase), mad or (not robust) sd.

biascorr

logical indicating whether a bias correction of the result should be done. Note that this bias correction is only valid for Gaussian processes.

...

further arguments passed to the function scalefn.

Details

The function estimates the residual autocovariance, which is the usual acf of the robustly transformed time series. Using estimators for location and scale, which can be chosen by using the arguments locfn and scalefn, the time series is transformed by applying a psi function (currently only Huber and Tukey are possible). The tuning parameter for Huber's function is k = 1.37 and for Tukey's function k = 4.68 but both can be changed using the ... argument. For the meaning of the tuning parameters, see e.g. Dürre et al. (2015).

There is a simulation based consistency correction implemented for Gaussian time series and the preset tuning parameters.

Value

A named list of the following elements:

acfvalues

Numeric vector of estimated autocorrelations at the lags 1,...,lag.max.

are

numeric value giving the asymptotic relative efficiency (ARE) of the estimator as compared to the classical nonrobust estimator, under the assumption that the observations are uncorrelated and from a Gaussian distribution. The ARE is currently not available for this estimation approach and is therefore NA.

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: 10.1002/wics.1351.

See Also

The wrapper function acfrob.

Alternative acf subroutines: acfrob.GK, acfrob.filter, acfrob.multi, acfrob.partrank, acfrob.rank, acfrob.bireg, acfrob.trim.

Examples

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set.seed(1066)
tss <- arima.sim(model = list(ar = 0.3, ma = 0.5), n = 100)
acfrob(tss, approach = "RA")

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