Analysis of Financial Time Series, Third Edition

10.9 Appendix: Some Remarks on Estimation

The estimation of multivariate ARMA models in this chapter is done by using the time series program SCA of Scientific Computing Associates. The estimation of multivariate volatility models is done by using either the S-Plus package with FinMetrics or the Regression Analysis for Time Series (RATS) program or Matlab. Below are some run streams for estimating multivariate volatility models using the RATS program. A line starting with * means “comment” only.

Estimation of the Diagonal Constant-Correlation AR(2)–GARCH(1,1) Model for Example 10.5

The program includes some Ljung–Box statistics for each component and some fitted values for the last few observations. The data file is m-ibmspln.txt, which has two columns, and there are 888 observations.

all 0 888:1

open data m-ibmspln.txt

data(org=obs) / r1 r2

set h1 = 0.0

set h2 = 0.0

nonlin a0 a1 b1 a00 a11 b11 rho c1 c2 p1

frml a1t = r1(t)-c1-p1*r2(t-1)

frml a2t = r2(t)-c2

frml gvar1 = a0+a1*a1t(t-1)**2+b1*h1(t-1)

frml gvar2 = a00+a11*a2t(t-1)**2+b11*h2(t-1)

frml gdet = -0.5*(log(h1(t)=gvar1(t))+log(h2(t)=gvar2(t)) $

           +log(1.0-rho**2))

frml gln = gdet(t)-0.5/(1.0-rho**2)*((a1t(t)**2/h1(t)) $

    +(a2t(t)**2/h2(t))-2*rho*a1t(t)*a2t(t)/sqrt(h1(t)*h2(t)))

smpl 3 888

compute c1 = 1.22, c2 = 0.57, p1 = 0.1, rho = 0.1

compute a0 = 3.27, a1 = 0.1, b1 = 0.6

compute  a00 = 1.17, a11 = 0.13, b11 = 0.8

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

set fv1 = gvar1(t)                                                      ...