RATIO OF VARIANCE OF RESIDUALS

DESCRIPTION

This method differs from the other methods presented here in that instead of estimating the long-range dependence parameter H it estimates the parameter alpha characterizing the intensity of heavy tails. The method is based on the Variance of Residuals method. It calculates the Variance of Residuals in two ways, and takes their ratio to obtain a statistic, and then fits a least-squares line to the logarithm of that statistic. This enables one to estimate alpha. The method is explained more fully below.

GRAPHICAL OUTPUT

- FARIMA(1,d,1) with Gaussian Innovations. alpha=2.0
- FARIMA(1,d,1) with Symmetric Stable Innovations. alpha=1.5
- Ethernet Byte Data
- Ethernet Packet Data

IMPLEMENTATION

There are several options available for using the ratio method.

- The cut-off points for the estimation can be set. (
*power1, power2*). -
*nvar*is the number of different levels to use in estimation. - 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*).