acfrob.multi: Robust Autocorrelation Estimation Based on Correlation...

In robts: Robust Time Series Analysis

Description

Robustly estimates the autocorrelation function of a time series based on robust estimators of the covariance matrix. 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 = "acfmulti".

Usage

acfrob.multi(x, lag.max, multi.method=c("weightedMCD", "rawMCD", "Stahel-Donoho", "S",
         "reweight", "Tyler", "M", "sscor"), ...)

Arguments

x	univariate numeric vector or time series object.
lag.max	integer value giving the maximum lag at which to calculate the acf.
multi.method	character string indicating the multivariate covariance estimator to be used. Must be one of 'weightedMCD' (the default), 'rawMCD', 'Stahel-Donoho', 'S', 'M', 'reweight' and 'Tyler', see Details.
...	additional arguments passed to the respective multivariate covariance estimator, see Details.

Details

This function estimates the autocorrelation function based on multivariate correlation estimators. This method computes the acf en bloc and is therefore very time consuming if lag.max is large (e.g. greater 15). The approach works very well in case of outliers occurring in blocks, see Dürre et al. (2015) for more details.

There are several possible robust correlation estimators available. The argument multi.method specifies which of the following approaches is to be used, where multi.method = "weightedMCD" is the default.

"rawMCD"

One applies the MCD proposed by Rousseeuw (1985). This estimator is known to be very robust but also inefficient under normality. Therefore one often uses reweighted versions. See the help page of covMcd for more details.

"weightedMCD"

One applies the weighted MCD, which is basically the empirical covariance of observations which are not identified as outliers. The identification is based on Mahalanobis distances calculated from the raw MCD, see covMcd for more details. For acf estimation the weighted MCD is preferable to the unweighted one, see Dürre et al. (2015).

"reweight"

One applies the efficient weighted MCD which was proposed by Gervini (2003). See the help page of Corefw for more details.

"Stahel-Donoho"

One applies the Stahel-Donoho estimator proposed by Stahel (1981) and Donoho (1982). See the help page of CovSde for more details. Note that this estimator gets really time consuming if lag.max is large!

"S"

One applies an S estimator of scatter proposed by Davies (1987). See the help page of CovSest for more details.

"M"

One applies an M estimator of scatter. Note that the breakdown point of M estimators decreases with incresing dimension (Maronna et al. 2006), so the estimator gets less robust for large lag.max. See the help page of mvhuberM for more details.

"Tyler"

One applies the Tyler shape matrix, which is a special M estimator of scatter (Tyler, 1987). See the help page of tyler.shape for more details.

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

Davies, P. (1987): Asymptotic behaviour of S-estimates of multivariate location parameters and dispersion matrices, Annals of Statistics, vol 15, 1269–1292.

Donoho, D.L. (1982): Breakdown properties of multivariate location estimators, PH.D. thesis at Harvard University.

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.

Gervini, D. (2003): A robust and efficient adaptive reweighted estimator of multivariate location and scatter, Journal of Multivariate Analysis, vol. 84, 116–144, doi: 10.1016/S0047-259X(02)00018-0.

Maronna, R., Martin, D., Yohai, V. (2006): Robust Statistics - Theory and Methods.

Rousseeuw, P.J. (1985): Multivariate estimation with high breakdown point, Mathematical Statistics and Applications Vol. B, 283–297, doi: 10.1007/978-94-009-5438-0_20.

Stahel, W. (1981): Infitisimal optimality and covariance matrix estimators, Ph.D. thesis at ETH Zürich.

Tyler, D.E. (1987): A disribution-free M-estimator of multivariate scatter, Annals of Statistics, vol. 15, 234–251.

See Also

The wrapper function acfrob.

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

Robust multivariate scatter estimators: covMcd, Corefw, CovSde, CovSest, mvhuberM, tyler.shape.

Examples

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

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