Absolute Moments

DESCRIPTION

This method plots the logarithm of the absolute moment of an aggregated (averaged) process versus the logarithm of the aggregation level. A least-squares line is fitted to the data, and the slope provides an estimate of H. This method is also useful in determining whether a multifractal structure is present.

GRAPHICAL OUTPUT

- First Absolute Moment for FGN (with H = 0.7)
- Third Absolute Moment for FGN (with H = 0.7)
- Ethernet Byte Data (First Absolute Moment)
- Ethernet Packet Data (First Absolute Moment)

IMPLEMENTATION

There are several options available for using the absolute moments
method. Either the function ** plotmoment **, which subtracts the mean of
the series, or the function ** plotmoment2 **, which does not subtract
the mean, can be used. Their options are the same.

- 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 minimum number of points to use in estimating the sample variance
can be set. (
*minnpts*, default = 5) - The fitted line whose slope is moment*(H-1) can be drawn or not.
(
*slopes*, default = YES) - 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) - Which moment is used is set by (
*moment*, default = 2).