acfrob.GK: Robust Autocorrelation Estimation Based on the Gnanadesikan...

In robts: Robust Time Series Analysis

Description

Robustly estimates the autocorrelation function (acf) of a time series based on Gnanadesikan Kettenring (GK) estimators. See Ma and Genton (2000) for details.

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

Usage

acfrob.GK(x, lag.max, scalefn = Qn, ...)

Arguments

x	univariate numeric vector or time series object.
lag.max	integer value giving the maximum lag at which to calculate the acf.
scalefn	function which calculates a scale estimator. Its first 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.
...	further arguments passed to the function scalefn.

Details

This function estimates the autocorrelation function based on the GK approach, which was proposed by Ma and Genton (2000). The acf is estimated for each lag individually. Let X denote the original time series and Y the lagged one, then the autocorrelation is estimated by

\frac{\hat{σ}(X+Y)^2-\hat{σ}(X-Y)^2}{\hat{σ}(X+Y)^2+\hat{σ}(X-Y)^2}.

If one uses the empirical standard deviation as the scale estimator sigma-hat, one roughly gets the usual empirical acf.

There are several possible scale estimators available. The argument scalefn specifies which estimator is to be used, where scalefn = Qn is the default. One could for example choose one of the following estimators.

Qn

The Qn is used, which was proposed by Rousseeuw and Croux (1993). The estimator is known to be very robust and also rather efficient under normality. See the help page of Qn in the package robustbase for details.

scaleTau2

The tau estimator of scale is used, which was proposed by Maronna and Zamar (2002). The estimator is also known to be robust and rather efficient under normality. The estimator includes two tuning parameters, which can be changed using the ... argument. See the help page of scaleTau2 in the package robustbase for more details.

mad

One uses the usual median absolute deviation, which is known to be very robust and fast to compute, but not very efficient under normality. For more details see the help page of mad in the package stats.

reweightedQn

One uses an efficiently reweighted Qn. For more details see the help page of reweightedQn.

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.

Author(s)

Alexander Dürre, Tobias Liboschik and Jonathan Rathjens

References

Ma, Y. and Genton M. (2000): Highly robust estimation of the autocovariance function, Journal of time series analysis, vol. 21, 663–684, doi: 10.1111/1467-9892.00203.

Maronna, R. and Zamar, R. (2002): Robust estimates of location and dispersion for high-dimensional data sets, Technometrics, vol. 44, 307–317, doi: 10.1198/004017002188618509.

See Also

The wrapper function acfrob.

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

Examples

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

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