options crt;
name armaxc "ARMA(12,2) Example" ;
? 
? ARMA(12,2) estimation, using a method from 
? Andrew Harvey, The Econometric Analysis of Time Series (1990) p.273
?
? TSP 4.3 (September 1995)
? Author: Clint Cummins
?
?fetch e1;  ? (Pindyck & Rubinfeld data)
load ;
?
list bnames phi1-phi12 theta1-theta2 alpha;
param bnames;       ? zero starting values -- converges in 45 iterations
mmake b bnames;     ? to SSR = 135.27569
?
?   Try starting values from MicroTSP handbook, to verify their SSR
?   of 136.6999 (this checks).  After another 31 iterations, the 
?   solution above is reached (with a better SSR).
?
mmake b 1.1087608 -.3156806 .1159227 -.1885951 .4076379 -.3692521
.1075082 .0634516 .1786308 -.2201502 .0850142 -.0038033
-.0007017 .0024705
-.3528025
;
unmake b bnames;
?
frml equ u = e1 - alpha;
genr equ;
copy @smpl usmpl;
?
?   Equation for residual
?
frml eqe e = u - phi1*u(-1) - phi2*u(-2) - phi3*u(-3) - phi4*u(-4)
               - phi5*u(-5) - phi6*u(-6) - phi7*u(-7) - phi8*u(-8)
               - phi9*u(-9) - phi10*u(-10) - phi11*u(-11) - phi12*u(-12)
               - theta1*e(-1) - theta2*e(-2);

?   Equations for derivatives of residual with respect to parameters

frml d1 dedp1 = -u(-1) - theta1*dedp1(-1) - theta2*dedp1(-2);
frml d2 dedp2 = -u(-2) - theta1*dedp2(-1) - theta2*dedp2(-2);
frml d3 dedp3 = -u(-3) - theta1*dedp3(-1) - theta2*dedp3(-2);
frml d4 dedp4 = -u(-4) - theta1*dedp4(-1) - theta2*dedp4(-2);
frml d5 dedp5 = -u(-5) - theta1*dedp5(-1) - theta2*dedp5(-2);
frml d6 dedp6 = -u(-6) - theta1*dedp6(-1) - theta2*dedp6(-2);
frml d7 dedp7 = -u(-7) - theta1*dedp7(-1) - theta2*dedp7(-2);
frml d8 dedp8 = -u(-8) - theta1*dedp8(-1) - theta2*dedp8(-2);
frml d9 dedp9 = -u(-9) - theta1*dedp9(-1) - theta2*dedp9(-2);
frml d10 dedp10 = -u(-10) - theta1*dedp10(-1) - theta2*dedp10(-2);
frml d11 dedp11 = -u(-11) - theta1*dedp11(-1) - theta2*dedp11(-2);
frml d12 dedp12 = -u(-12) - theta1*dedp12(-1) - theta2*dedp12(-2);
frml d13 dedt1 = -e(-1) - theta1*dedt1(-1) - theta2*dedt1(-2);
frml d14 dedt2 = -e(-2) - theta1*dedt2(-1) - theta2*dedt2(-2);
frml d15 deda = -1+phi1+phi2+phi3+phi4+phi5+phi6
                +phi7+phi8+phi9+phi10+phi11+phi12
                - theta1*deda(-1) - theta2*deda(-2);
list deqs d1-d15;
list dvars dedp1-dedp12 dedt1-dedt2 deda;
?
?  zero the presample values
?
smpl 60:11 88:6;
dot e dvars;
  . = 0;
enddot;
?
smpl 61:1 88:6;                ? u exists from 60:1 ; use 12 lags
genr eqe;
copy @smpl esmpl;
mat ssrold = e'e;
print ssrold;
?
mat novar = nrow(b);
supres @logl @nob @coef @smpl;
const maxit,50 maxsqz,10 tol,.001;
  do iter=1,maxit;
    dot deqs;
       genr(silent) .;
     enddot;

     ? Gauss-Newton iteration:  regress e on derivatives

     ols(silent) e dvars;
     rename @coef delt;

     ? test for convergence and squeeze to find stepsize.

     mat worst = max(abs(delt)/(abs(b) + 10*tol));
     if worst<tol; then; goto 20;
     do isqz=1,maxsqz;
       mat testb = b - delt/(4**(isqz-1));
       unmake testb bnames;
       smpl usmpl;
       genr(silent) equ;
       smpl esmpl;
       genr(silent) eqe;
       mat ssrnew = e'e;
       ?write ssrold ssrnew isqz;
       if ssrnew<ssrold; then; goto 15;
     enddo;

     write(form='(" Failure to improve after ",F4.0," squeezes.")') isqz;
     write b delt;
     goto 18;
 
15   write iter,ssrnew;
     set ssrold = ssrnew;
     copy testb b;
   enddo;

18 write(form='(" Failure to converge after ",F4.0," iterations.")') iter;
   goto 30;

20 write(form='(" Convergence after ",F4.0," iterations.")') iter;

30 unmake b bnames;
   write ssrold bnames;
   nosupres @coef;
   tstats(names=bnames) b @vcov;
   uhat = u - e;
   corr(silent) u uhat;
   set rsq = @corr(2,1)**2;
   print rsq;
stop ; end ;
freq m ;
smpl 60:1 88:6 ;
noprint ; 
load e1 ;
2.97763
1.779284
.139459
-0.300253
-0.209599
-0.618679
-0.974983
-0.39654
.00197016
-0.633105
-0.405974
-0.862646
-1.07628
-0.366386
-0.378376
-0.338074
.125675
.352397
.32847
.242852
-0.178227
-0.676851
-0.23684
.00253383
-0.233415
-0.743753
-0.243722
-0.509275
-0.40045
-0.169629
-0.0490396
.021424
-0.350644
-0.827592
-0.57201
-0.380863
-0.22728
.270134
.181951
.0325734
.0812054
.0820162
-0.240734
-0.305646
-0.245724
.117606
.289217
.265986
-0.104321
.028213
.167167
.00629333
.318632
.362087
.0162988
.150604
.078022
-0.238707
-0.576766
.673539
.118824
.208336
-0.0922454
.0285369
-0.382192
-0.469423
-0.61247
-0.654158
-0.647197
-0.362114
.122077
.0801545
.210863
.046701
-0.41081
-0.215858
-0.198224
-0.254579
.239089
.0085099
.367707
.533627
.481672
.349429
.543094
.226255
-0.555229
-0.719662
-0.721777
-0.934846
-0.283929
-0.549704
-0.0491925
-0.196619
.428831
.669973
.189711
-0.219671
-0.350394
-0.189788
.392836
.479683
.314343
-0.0539162
.235469
.294032
.380029
1.115388
.762898
.783421
.361121
.330352
-0.0416012
.341438
1.217469
1.153705
1.31649
1.349372
1.829828
2.056906
1.94941
1.023223
.436914
.726692
1.194206
1.279735
1.095738
1.01862
.998999
.573831
-0.254264
-0.146974
-0.161421
-1.228215
-2.147969
-1.834865
-1.596318
-0.878091
-0.0427138
-0.6476
-1.099259
-0.523404
-0.897972
-1.065581
-1.674996
-2.026828
-2.315016
-2.426637
-2.229585
-2.455464
-2.037928
-2.269594
-1.381174
-1.351681
-1.058814
-0.787299
-0.970658
-1.569739
-1.875673
-2.792105
-2.091152
-1.395624
-0.574112
.990906
-1.10465
-0.94208
.520289
-0.02753
1.532141
-1.02011
-1.186153
-1.102502
-0.946006
-0.18329
-0.159202
.283704
-1.587271
-1.880342
-2.444218
-1.82832
-1.565346
-1.825066
-0.515746
.269658
-0.0402539
-0.138299
.692353
-0.051465
.364685
-0.454288
-1.310706
-0.513368
-1.260725
-0.939849
-0.49087
-1.437122
-1.091236
-0.855651
-1.723984
-1.796976
-1.413496
-1.796581
-1.552578
-1.844401
-2.025218
-2.092561
-2.514871
-2.937661
-2.696879
-2.966828
-2.24697
-1.639027
-0.836093
-0.416128
-0.747783
-1.019779
-0.9686
-1.101324
-1.576499
-1.533164
-1.4873
-1.696718
-1.262401
-1.226698
-0.11121
.247768
.603285
.951482
.926043
.343824
.590976
.0564743
-0.130777
-0.117753
.408646
.552875
1.600688
2.8531
2.325351
2.946109
2.729154
3.46666
5.75996
3.137593
-1.906262
-2.090536
.246624
1.202378
2.406778
3.498187
4.873793
7.52603
6.391669
5.849452
4.723364
4.733202
7.138319
5.972295
6.533319
7.512002
6.714649
5.583079
2.855017
3.503785
4.986651
5.846635
5.42409
4.864418
4.534905
5.338166
4.286859
1.472186
.953441
.986149
1.334087
1.620203
1.184824
1.649697
1.80182
1.613026
1.538118
1.983785
2.017906
2.273251
1.458404
1.063102
.777605
1.030473
1.095038
1.45497
1.306785
1.096925
1.135772
1.326309
1.821627
2.179321
2.076571
1.623153
.394518
.166076
-0.339501
-0.0249895
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-0.0570244
-0.748696
-1.20585
-1.130474
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-3.310998
-3.635184
-3.521743
-3.603326
-3.799256
-3.505364
-3.305545
-3.478082
;