WHITTLE

SAMPLE RUN ONE

# Denotes comments added after the session.

# In S-Plus:

> X11()                  # Enable  graphics window.
> source("whittle.S")	 # Read in the program.
> z <- scan(file="data") # Read in file called data and assign to vector z.
> h1 <- whittle(z,model="fgn")
	                 # Do the Whittle method with a FGN model and 
			 #  assign result to h1.
			 #Intermediate results of the minimization.  etatry
			 # is H, B is the value being minimized.
etatry= 0.5 B= 1.00022927893032
etatry= 0.500000014901161 B= 1.00022925550517
etatry= 0.999 B= 1.02218824080293
etatry= 0.742705939789286 B= 0.884005310343698
etatry= 0.742705053700002 B= 0.884005156062208
etatry= 0.718504838680966 B= 0.880828221477977
etatry= 0.718505168437669 B= 0.880828250207842
etatry= 0.694266514080424 B= 0.879860064932244
etatry= 0.694266980348998 B= 0.879860060786826
etatry= 0.696510889409528 B= 0.879850585969451
etatry= 0.696510445274812 B= 0.879850585779315
etatry= 0.696407782606995 B= 0.879850563700104
etatry= 0.696408237954346 B= 0.879850563701856
etatry= 0.696407327259644 B= 0.879850563699207
etatry= 0.696407077341415 B= 0.879850563699092
etatry= 0.696416131546077 B= 0.87985056386839
etatry= 0.696398023136753 B= 0.879850563868667
theta= 0.140032566394901 0.696407077341415
H= 0.696407077341415                   #Estimated H.
95%-C.I. for H: [ 0.683541807805226 , 0.709272346877604 ]
95%-C.I.:
        etalow     etaup               #Approximate 95% confidence intervals
[1,] 0.6835418 0.7092723               # for H.
 
> h1[[1]]$parameter                    #h1 contains the parameter estimate.
[1] 0.6964071                          #[[1]] is necessary for the case where
				       #several subseries are used, to distin-
				       #guish them.

SAMPLE RUN TWO

 
> h2 <- whittle(data,out=F)
		#Now we run the estimator with a FARIMA(1,d,1) model (Default).
		#The intermediate output is not produced.
>h2[[1]]$parameter
                #Output the estimate.
[1]  0.6940678  0.0369692 -0.0334319
                #Contains the estimated: H, and phi_1 and theta_1 for the
		#(1,d,1) model.

>q()                                         # Quit.

SAMPLE RUN THREE

# Denotes comments added after the session.

# In S-Plus:

z1 <- rep(0,1000)        # Initialize vector.
for ( i in 1:1000){
   z1[i] <- 1/10*sum(z[(10*i-9):(10*i)])}
                         # Aggregate the vector z by a factor of 10.

> h3 <- whittle(z1,model="fgn")
	                 # Do the Whittle method with a FGN model and 
			 # the aggregated series z1, assign result to h3.
			 #Intermediate results of the minimization.  etatry
			 # is H, B is the value being minimized.
etatry= 0.5 B= 1.00049318502577
etatry= 0.500000014901161 B= 1.00049316047897
etatry= 0.999 B= 0.990106893837151
etatry= 0.998999062241329 B= 0.990104299949572
etatry= 0.7495 B= 0.862081752334782
etatry= 0.749500294232016 B= 0.862081788105388
etatry= 0.738029903867731 B= 0.860922000220984
etatry= 0.738030172460806 B= 0.860922021808059
etatry= 0.715655615675116 B= 0.860067724273093
etatry= 0.715656076822042 B= 0.860067721857196
etatry= 0.717024808865672 B= 0.860064289453432
etatry= 0.717024362086441 B= 0.860064289356667
etatry= 0.716970451671377 B= 0.860064283504803
etatry= 0.716971326385792 B= 0.860064283507541
etatry= 0.716969576956961 B= 0.860064283505106
etatry= 0.716970100010298 B= 0.860064283504558
etatry= 0.716979577031209 B= 0.860064283683035
etatry= 0.716960622989387 B= 0.860064283683146
theta= 0.13688348209654 0.716970100010298
H= 0.716970100010298
95%-C.I. for H: [ 0.676137287998876 , 0.75780291202172 ]
95%-C.I.:
        etalow     etaup               #Approximate 95% confidence intervals
[1,]    0.6761373 0.7578029            # for H.
 
> h3[[1]]$parameter                    #h3 contains the parameter estimate.
[1]    0.7169701                       #[[1]] is necessary for the case where
				       #several subseries are used, to distin-
				       #guish them.