R/S

DESCRIPTION

The R/S statistic originally arose in connection with hydrological data. It provides a graphical method of estimating the long-range dependence parameter H by fitting a least squares line to the values of a statistic computed at many different points. It is explained more fully below.

GRAPHICAL OUTPUT

- Fractional Gaussian Noise (H = 0.7)
- Fractional Gaussian Noice (H = 0.7, with more options)
- Fractional Gaussian Noise (H=0.7), with Modified Lo's R/S
- Ethernet Byte Data
- Ethernet Packet Data

IMPLEMENTATION

The R/S method has many different options, depending on exactly what the practitioner wishes to do. Some of them are listed below.

- The cut-off points for the estimation can be set. They should be
chosen to define a linear range. (
*power1*and*power2*, defaults = 10^(0.7), 10^(2.5)) - The data can be shuffled at random, to determine whether it is the
correlation structure or the marginal distribution which is causing certain
effects. (
*shuffle*, default = NO) - One can either let the lag values become greater than the block length,
or not. If they do become greater than the block length, then there are
data points which are used more than once, and overlap occurs.
(
*overlap*, default = YES) - The data can be differenced an integer number of times before applying
R/S. (
*ndiff*, default = NO) - The data can be differenced at a lag other than 1. (
*nlag*, default = NO) - R/S, or just R can be computed and H estimated. (
*rflag*, default = R/S) - When more than one block is being used, the points within each block
can be connected, and separate estimates of H for each block obtained, as
well as the overall estimate. This is particularly useful if
non-stationarity is suspected. (
*connect*, default = NO) - A regular least-squares fit can be done for the pox plot, or a
robustified least-squares fit can be done. This is also particularly
useful in the case of suspected non-stationarities. (
*fitls*, default = regular least-squares) - Just an estimate can be obtained, or the graphical plot as well. The
latter is always recommended when an unknown series is being examined. The
former can be used in lengthy simulation studies, etc. (
*plotflag*, default = YES) - If Lo's R/S is to be used, the routine
**rsfunc**can be used. The only option is the q which is to be used (*maxlag*). - If Modified Lo's R/S is to be used (Lo's R/S with multiple q),
**plot.lo**is used. The options are (*mult*) which controls the spacing between values of q, and (*n*) which controls the number of q's to use. (Maximum q = mult*n). A plot is produced, plotting the statistic vs. q, and showing the confidence intervals for the null hypothesis of no long-range dependence.