acfrob.median: Robust Autocorrelation Estimation Based on Median Correlation

In robts: Robust Time Series Analysis

Description

Robustly estimates the autocorrelation function of a time series based on the median correlation. See Chakhchoukh (2010) for details.

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

Usage

acfrob.median(x, lag.max, 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.
biascorr	logical indicating whether a bias correction of the result should be done. Note that this bias correction is only valid for Gaussian processes.

Details

This function estimates the autocorrelation function based on the median correlation, which is proposed by Chakhchoukh (2010). 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

median(XY)/median(X^2).

The resulting value does not measure the usual autocorrelation. Therefore a nonlinear transformation based on a Monte Carlo simulation is applied, which is only valid for Gaussian processes.

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

Chakhchoukh, Y. (2010): A new robust estimation method for ARMA models, IEEE Transactions on Signal Processing, vol. 58, 3512–3522, doi: 10.1109/TSP.2010.2046413.

See Also

The wrapper function acfrob.

Alternative acf subroutines: acfrob.GK, 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 = "median")

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