*
* Example 10.3 from pp 452-453
*
calendar(m) 1965
open data m-mrk6503.txt
data(format=free,org=columns) 1965:1 2003:12 time mrk
open data m-pfe6503.txt
data(format=free,org=columns) 1965:1 2003:12 time pfe
*
* BEKK models are notoriously difficult to estimate because all the coefficients
* enter in squared form. As a result, none of them are globally identified (flip
* the signs of any of the matrices and the fit doesn't change), and there tend to
* be several local modes. Because derivative-based methods (such as the default
* METHOD=BFGS on GARCH) tend to lose their ways in such situations, we recommend
* the use of a preliminary set of iterations with METHOD=SIMPLEX to refine the
* initial guess values. Although the estimates from the GARCH below look quite a
* bit different from those for the DVEC, they have a higher likelihood and pass
* the multivariate Q test on the squares.
*
garch(p=1,q=1,mv=bekk,hmatrices=hh,rvector=rr,piters=10,pmeth=simplex,iters=200) / pfe mrk
set hpfe = sqrt(hh(t)(1,1))
set hmrk = sqrt(hh(t)(2,2))
set rho  = hh(t)(1,2)/(hpfe*hmrk)
*
spgraph(vfields=3,footer="Figure 10.5 Estimate volatilities and time-varying correlations of a DVEC(1,1) model")
graph(header="(a) PFE volatility")
# hpfe
graph(header="(b) MRK volatility")
# hmrk
graph(header="(c) Time-varying correlations")
# rho
spgraph(done)
*
set stdpfe = rr(t)(1)/sqrt(hh(t)(1,1))
set stdmrk = rr(t)(2)/sqrt(hh(t)(2,2))
@regcorrs(number=12) stdpfe
@regcorrs(number=12) stdmrk
set stdpfesq = stdpfe**2
set stdmrksq = stdmrk**2
@regcorrs(number=12) stdpfesq
@regcorrs(number=12) stdmrksq
*
@mvqstat(lags=10)
# stdpfe stdmrk
@mvqstat(lags=10)
# stdpfesq stdmrksq