AGGREGATED VARIANCE

DESCRIPTION

This method plots the logarithm of the variance 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.

A more detailed description.

GRAPHICAL OUTPUT

• Fractional Gaussian Noise (with H = 0.7)
  The function B + (2H-2) log m is fitted to the log of the variances.

  Differenced Variance With Fractional Gaussian Noice (with H = 0.7)

  The function B + (2H-2) log m is fitted to the log of the differenced variances.

  Fractional Gaussian Noise (with H = 0.7) (using modifed version)

  The function A + B m^(2H-2) is fitted to the variances.

  Ethernet Byte Data

  Ethernet Packet Data

IMPLEMENTATION

There are several options available for using the aggregated variance method.

1. 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))
2. The minimum number of points to use in estimating the sample variance can be set. (minnpts, default = 5)
3. The fitted line whose slope is 2H-2 can be drawn or not. (slopes, default = YES)
4. 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)
5. The variance can be differenced if non-stationarity suspected. (diff, default = NO)
6. The routine (plotvar2) can be used instead if non-stationarity suspected. This routine fits a function of form A+Bm^(2H-2) to the sample variance.

• Sample Runs
• Splus Source Code