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.

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. - The percentage of the data used in estimating H can be set (