asymvar.window: Calculation of the Long Run Variance Based on Subsampling

In robts: Robust Time Series Analysis

Description

Computes the long run variance, which is required for change point testing, based on subsampling. See Dehling et al. (2013) for details.

Usage

asymvar.window(x, overlapping = TRUE, obs = c("untransformed", "ranks"),
               dd = c("independent", "carlstein-cor", "carlstein-Qn"),
               momentp = 1)

Arguments

x	numeric vector or univariate time series object.
overlapping	logical indicating whether block sums should be distinct or overlapping, see Details.
obs	character string indicating whether the long run variance of a cusum statistic ("untransformed") or of a Wilcoxon statistic ("ranks") is calculated.
dd	character string indicating how the block length should be determined, see Details.
momentp	numeric value indicating what absolute centered mean is used to estimate the long run variance.

Details

Cusum-type change point tests require an estimation of the long run variance. One possibility is to use subsampling methods, where one splits the sample into blocks and estimates the variance by a centered absolute empirical moment of these block sums. There are different tuning options: setting the block length l, choosing the centered absolute moment p and characterising the block building. For the later, there are two options.

If overlapping is TRUE, one uses a n-l successive overlapping blocks. This method was proposed by Peligrad and Shao (1995). Otherwise, one uses \lfloor n/l \rfloor distinct blocks which was proposed by Carlstein (1986).

There are three different methods to determine a working block length l, which are chosen by the argument dd:

"carlstein-cor"

Use Carlstein's rule for an optimal block length. Therefore it is assumed that the time series follows an AR(1) model. See Carlstein (1986) for more Information.

"carlstein-Qn"

Basically apply Carlstein's rule with a robust estimation of the AR(1) coefficient. To be more specific, it is estimated by the autocorrelation of the first lag using acfrob.GK.

"carlstein-Qn"

independent

Use a thumb rule only based on the time series length n:

round((3N)^{1/3}+1).

Value

List containing the following named elements:

lrv	estimated long run variance
blocklength	used block length of the subsamples

Author(s)

Roland Fried and Alexander Dürre

References

Carlstein, E. (1986): The use of subseries values for estimating the variance of a general statistic from a stationary sequence, The Annals of Statistics, vol. 14, 1171–1179, doi: 10.1214/aos/1176350057.

Dehling, H., Fried, R., Shapirov, O., Wornowizki, M. (2013): Estimation of the variance of partial sums of dependent processes, Statistics and Probability Letters, vol. 83, 141–147, doi: 10.1016/j.spl.2012.08.012.

Peligrad, M., Shao, Q. (1995): Estimation of the Variance of Partial Sums for rho-Mixing Random Variables, Journal of Multivariate Analysis, vol. 152, 140–157, doi: 10.1006/jmva.1995.1008.

See Also

The long run variance can be also estimated by asymvar.acf and asymvar.acfextra.

Examples

set.seed(1066)
tss <- arima.sim(model = list(ar = 0.3, ma = 5), n = 100)
asymvar.window(tss)

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