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.
A more detailed description.
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.
To use the Fractal Dimension Method, the functions plotfract and
plotfract2 are provided. The first takes a series equivalent to
cumulated FGN (Fractional Brownian Motion), and the second takes FGN
itself. The options are the same as for the moment methods except that
minnpts and moment are not used.
- 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).