R/S

Periodogram

DESCRIPTION

This method plots the logarithm of the periodogram of a process versus the logarithm of the frequency. A least-squares line is fitted to the data, and the slope provides an estimate of H.
A more detailed description.

GRAPHICAL OUTPUT

Periodogram for FGN (with H = 0.7)
Modified Periodogram for FGN (with H = 0.7)
Modified Periodogram for Ethernet Byte Series
Modified Periodogram for Ethernet Packet Series
The periodogram plots were not produced for the Ethernet series because the graphics
take up a huge amount of memory when such long series are used.

IMPLEMENTATION

There are several options for using the periodogram method.

For the original periodogram, the routine plotper is used.
The percentage of the data used in estimating H can be set (percent). Default is 10%.
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 length simulation studies, etc. (plotflag, default = YES)
The averaged (cumulative) periodogram can be used via the routine plot.av.per, with the same options as plotper.
The modified periodogram can be used via the routine perbox. It has the following options:
(plotflag) as above.
(nbox, default=100) is the number of boxes to divide the data into.
(tempper, default = 1) is the fraction of points used in calculating slope.
(percent, default = 1%) is percentage of points in the beginning not to put into boxes.
Continuous version of periodogram can be used. This calculates the periodogram estimate of H for several values of percent , via the routine per.cont.
( plotflag ) as above.
( i ) is the number of different values to use.
( mult ) Changes the spacing. tempper = length(data)/mult * (1:i).
The routine per.theory.cont is as (4), but uses spectral density to compute the theoretical plot of continuous version of periodogram.
The routine cumper is the cumulative periodogram. Its parameters are im, the inverse of the upper cut-off, and l, the lower cut-off.