AGGREGATED VARIANCE

SAMPLE RUN ONE (FGN with H=0.7)

# Denotes comments added after the session.

# In S-Plus:

> X11()                  # Enable  graphics window.
> source("plotvar.S")    # Read in the program.
> z <- scan(file="data") # Read in file called data and assign to vector z.
> h1 <- plotvar(z)       # Do the default Variance  (Series length 10000) and
                         # assign result to h1, and get the first figure.

beta =  -0.578280790489008      # Slope of fitted line
 
H=  0.710859604755496           # Estimate of H

> h1                            # Estimate of H
 [1]  0.7108596

Graphical output.

SAMPLE RUN TWO (FGN with H=0.7, Differenced Variance)

> h2 <- plotvar(z,diff=1,power1=1,power2=2.2)
                #       Change values of some of the parameters and get
                #       second figure.  Differenced variance method now used.

May be problem with non-stationarity.  Taking differences of variances.
Beta =  -0.622504014937431      #       Slope of fitted line
H =  0.688747992531284          #       Estimate of H

> h2                            #       Estimate of H
[1] 0.688748

Graphical output.

SAMPLE RUN THREE (Bytes and Packets Ethernet data)

> h3 <- plotvar(tmsec829mb,power1=1,power2=4)
                #       Byte Ethernet data

 beta =  -0.424350263228253 
 
H=  0.787824868385874 

> h3                            #       Estimate of H
[1] 0.7878249

Graphical output. > h3 <- plotvar(tmsec829mp,power1=1,power2=4) # Packet Ethernet data beta = -0.300862534712653 H= 0.849568732643673 > h3 # Estimate of H [1] 0.8495687 Graphical output.

SAMPLE RUN FOUR (FGN with H=0.7, Modified Variance)

> h3_plotvar2(FGN7[1,])         # Use plotvar2 when non-stationarity suspected.
                                # Fits a curve of form  A + B*m^(2H-2).  
                                # Beta corresponds to 2H-2.

fit = 0.00244447882329504 0.946110275256865 -0.589447042843441 
Beta =  -0.589447042843441      # Slope of fitted line
H =  0.70527647857828           # Estimate of H

> h3                            # Estimate of H
[1] 0.7052765

>q()            # Quit.

Graphical output.