options double crt;
name egarch 'asymmetric EGARCH(1,1) benchmark from Brooks et al review';
?           RATS        SAS        TSP e(0)=mean     TSP  e(0)=0
?  mu     -.0117      -.0116      -.01167873487     -.01156255945
?         (.00886)    (.00866)    (.0083216274259)  (.0083218990687)
?  omega  -.127       -.127       -.12633933747     -.12634299469
?         (.0285)     (.0290)     (.02721344887)    (.02721413113)
?  beta    .912        .912        .91265373928      .91265496832
?         (.0168)     (.0172)     (.01617807763)    (.01617865944)
?  alpha   .333        .333        .33305592776      .33305812431
?         (.0406)     (.0423)     (.03875690246)    (.03875886989)
?  gamma  -.0385      -.0385      -.03845788444     -.03840128593
?         (.0192)     (----)      (.01829620652)    (.01830164351)
?  LogL   -1101.689   -1101.689   -1101.6843841     -1101.6761612
?--------------------
? - SEs for RATS and SAS are computed from the reported t-statistics
?   from a draft of Brooks, Burke and Persand, "Benchmarks and the
?   Accuracy of GARCH Model Estimation," International Journal of
?   Forecasting, forthcoming
? - LogL for RATS and SAS was computed by TSP at the coefficients
?   rounded to the 3 digits given, using e(0)=mean.
? - SEs for TSP are from numeric second derivatives
?   (This feature is not released yet, as of 3/16/00)
? - Convergence options were set in TSP to obtain the most accurate
?   results possible.  They appear to be accurate to 6-9 digits,
?   judging from the "change" vector from the final iteration.
? Presample values were set to:
? - h(0) = e'e/T , where e is computed from current mu value
? - e(0) = sum(e)/T, or 0
?---------
?  y = Deutschmark-British Pound daily percentage nominal returns,
?      1/3/1984 - 12/31/1991
?      Obtained on 1/30/98 from   ftp  web.amstat.org
?      jbes/View/96-2-APR/bollerslev_ghysels/bollerslev.sec41.dat
smpl 2,1975;
read(file='dmbp.dat') y monday;
olsq y c;

supres smpl;
copy @smpl smp2;
smpl 1,1975;
trend obs;
e = 0;
h = 0;
set pi = 4*atan(1); print pi;
set r2opi = sqrt(2/pi);
smpl smp2;

param mu -.01 omega -.1 beta .9 alpha .3 gamma -.04;
options nwidth=20,signif=10;
set eopt=1;
ml(hiter=u,hcov=u,tol=1e-15) eg11 mu omega beta alpha gamma;

title 'e(0) = e_mean';
ml(hiter=u,hcov=u,grad=c4,tol=1e-15) eg11 mu omega beta alpha gamma;

title 'e(0) = 0';
set eopt=0;
ml(hiter=u,hcov=u,grad=c4,tol=1e-15) eg11 mu omega beta alpha gamma;

title 'LogL for RATS';
param mu -.0117 omega -.127 beta .912 alpha .333 gamma -.0385;
set eopt=1;
eg11;
print @logl;
mmake coef mu omega beta alpha gamma;
mmake tstat -1.32 -4.46 54.4 8.20 -2.01;
mat serat = coef/tstat;
print serat;

title 'LogL for SAS';
param mu -.0116 omega -.127 beta .912 alpha .333 gamma -.0385;
set eopt=1;
eg11;
print @logl;
mmake coef mu omega beta alpha gamma;
mmake tstat -1.34 -4.38 53.0 7.88 1000;
mat sesas = coef/tstat;
print sesas;

proc eg11;
  smpl smp2;
    e = y-mu;
    mat ssr = e'e;
    set h0 = ssr/@nob;
    mat e0 = sum(e)/@nob;
  smpl 1,1;
    h = h0;
    if eopt; then; e = e0;
  smpl smp2;
    h = exp(omega + beta*log(h(-1)) + gamma*e(-1)/sqrt(h(-1)) +
            alpha*[abs(e(-1))/sqrt(h(-1)) - r2opi] );
    logl = -log(h)/2 + lnorm(e/sqrt(h));
    mat @logl = sum(logl);
endproc;