Analysis of Financial Time Series, Third Edition

Appendix C: Some RATS Programs for Duration Models

The data used are adjusted time durations of intraday transactions of IBM stock from November 1 to November 9, 1990. The file name is ibm1to5.txt and it has 3534 observations.

Program for Estimating a WACD(1,1) Model

all 0  3534:1

open data ibm1to5.txt

data(org=obs) / x r1

set psi = 1.0

nonlin a0 a1 b1 al

frml gvar = a0+a1*x(t-1)+b1*psi(t-1)

frml gma = %LNGAMMA(1.0+1.0/al)

frml gln =al*gma(t)+log(al)-log(x(t)) $

  +al*log(x(t)/(psi(t)=gvar(t)))-(exp(gma(t))*x(t)/psi(t))**al

smpl 2 3534

compute a0 = 0.2, a1 = 0.1, b1 = 0.1, al = 0.8

maximize(method=bhhh,recursive,iterations=150) gln

set fv = gvar(t)                      

set resid = x(t)/fv(t)

set residsq = resid(t)*resid(t)

cor(qstats,number=20,span=10) resid

cor(qstats,number=20,span=10) residsq

Program for Estimating a GACD(1,1) Model

all 0  3534:1

open data ibm1to5.txt

data(org=obs) / x r1

set psi = 1.0

nonlin a0 a1 b1 al ka

frml cv = a0+a1*x(t-1)+b1*psi(t-1)

frml gma = %LNGAMMA(ka)

frml lam = exp(gma(t))/exp(%LNGAMMA(ka+(1.0/al)))

frml xlam = x(t)/(lam(t)*(psi(t)=cv(t)))

frml gln =-gma(t)+log(al/x(t))+ka*al*log(xlam(t))

   -(xlam(t))**al

smpl 2 3534

compute a0 = 0.238, a1 = 0.075, b1 = 0.857, al = 0.5, ka = 4.0

nlpar(criterion=value,cvcrit=0.00001)

maximize(method=bhhh,recursive,iterations=150) gln

set fv = cv(t)                      

set resid = x(t)/fv(t)

set residsq = resid(t)*resid(t)

cor(qstats,number=20,span=10) resid

cor(qstats,number=20,span=10) residsq

Program ...