options crt;   
name armax7 "Reproduce Pindyck & Rubinfeld ARMAX results (pp.554-560)" ;
?
?   This example illustrates the estimation of a Transfer Function 
?   Model (ARMA with right hand side predetermined variables). 
?   The example is given in the Third Edition of Pindyck and Rubinfeld,
?   pages 554-560. 
?
?   TSP 4.3 (September 1995)
?   Author: Clint Cummins
?
freq m;
smpl 59:1 88:6;       
load;
smpl 59:2 88:6;
                             ? fygm3 is the 3 month T-bill rate.
inf = log(pw/pw(-1));        ? PPI growth rate.
gip = log(ip/ip(-1));        ? Industrial production index growth.
gm = log(fm1/fm1(-1));       ? M1 growth rate.
smpl 60:1 88:6;
ols fygm3 c gm(-1) ip(-1) gip(-1) inf(-1)-inf(-4);
?
unmake @coef alpha b1-b7;
frml equ u = fygm3 - (alpha + b1*gm(-1) + b2*ip(-1) + b3*gip(-1) +
             b4*inf(-1) + b5*inf(-2) + b6*inf(-3) + b7*inf(-4) );
copy @res u;
copy @smpl usmpl;
smpl 88:1 88:6;
plot (device=char) fygm3 y @fit p;
?
? ARMA(12,2) estimation. See the following reference for the method.
? Andrew Harvey, The Econometric Analysis of Time Series (1993), p.273.
?
list bnames phi1-phi12 theta1-theta2 alpha b1-b7;
param bnames;
Param
PHI1  1.51942  PHI2  -1.48756 PHI3  1.02639 PHI4  -.454318
PHI5  .566585 PHI6  -.649782 PHI7  .509403 PHI8  -.211461
PHI9  .208973 PHI10 -.219305 PHI11 .219001 PHI12 -.066680
THETA1  -.423494 THETA2  .744002 ;  ? from ARMA(12,2) on U
mmake b bnames;
?
?  The above starting values yield a failure to improve after
?  15 iterations, with SSR = 72.91861 and RSQ = .97384 .
?
?  Try the MicroTSP results as starting values (to try to verify their
?  SSR of 72.84838).  TSP gets 72.86518 from these starting values.
?  From these starting values, TSP uses 41 more iterations, to yield
?  SSR = 71.96000, which is better. 
?
mmake b 1.1772271 -.1137702 -.1876244 .0429768 .1803851 -.2845974
 .0247142 .2843771 .0207156 -.1959623 .0392602 .0081196
 .2140103 -.2755441
 -17.735207 13.974195 .1779367 -8.0316065 9.0408316 6.7157396
 6.2660084 -3.3522356
;
unmake b bnames;
smpl usmpl;
genr equ;
?
?   Equation for disturbance.

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 disturbance wrt 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);

?ols fygm3 c gm(-1) ip(-1) gip(-1) inf(-1)-inf(-4);

frml d15 deda = -1+phi1+phi2+phi3+phi4+phi5+phi6+
                   phi7+phi8+phi9+phi10+phi11+phi12
                - theta1*deda(-1) - theta2*deda(-2);
frml d16 dedb1 = -gm(-1)+phi1*gm(-2)+phi2*gm(-3)+phi3*gm(-4)+phi4*gm(-5)
                 +phi5*gm(-6)+phi6*gm(-7)+phi7*gm(-8)+phi8*gm(-9)
                 +phi9*gm(-10)+phi10*gm(-11)+phi11*gm(-12)+phi12*gm(-13)
                 - theta1*dedb1(-1) - theta2*dedb1(-2);
frml d17 dedb2 = -ip(-1)+phi1*ip(-2)+phi2*ip(-3)+phi3*ip(-4)+phi4*ip(-5)
                 +phi5*ip(-6)+phi6*ip(-7)+phi7*ip(-8)+phi8*ip(-9)
                 +phi9*ip(-10)+phi10*ip(-11)+phi11*ip(-12)+phi12*ip(-13)
                 - theta1*dedb2(-1) - theta2*dedb2(-2);
frml d18 dedb3 = -gip(-1)+phi1*gip(-2)+phi2*gip(-3)+phi3*gip(-4)+phi4*gip(-5)
                 +phi5*gip(-6)+phi6*gip(-7)+phi7*gip(-8)+phi8*gip(-9)
                 +phi9*gip(-10)+phi10*gip(-11)+phi11*gip(-12)+phi12*gip(-13)
                 - theta1*dedb3(-1) - theta2*dedb3(-2);
frml d19 dedb4 = -inf(-1)+phi1*inf(-2)+phi2*inf(-3)+phi3*inf(-4)+phi4*inf(-5)
                 +phi5*inf(-6)+phi6*inf(-7)+phi7*inf(-8)+phi8*inf(-9)
                 +phi9*inf(-10)+phi10*inf(-11)+phi11*inf(-12)+phi12*inf(-13)
                 - theta1*dedb4(-1) - theta2*dedb4(-2);
frml d20 dedb5 = -inf(-2)+phi1*inf(-3)+phi2*inf(-4)+phi3*inf(-5)+phi4*inf(-6)
                 +phi5*inf(-7)+phi6*inf(-8)+phi7*inf(-9)+phi8*inf(-10)
                 +phi9*inf(-11)+phi10*inf(-12)+phi11*inf(-13)+phi12*inf(-14)
                 - theta1*dedb5(-1) - theta2*dedb5(-2);
frml d21 dedb6 = -inf(-3)+phi1*inf(-4)+phi2*inf(-5)+phi3*inf(-6)+phi4*inf(-7)
                 +phi5*inf(-8)+phi6*inf(-9)+phi7*inf(-10)+phi8*inf(-11)
                 +phi9*inf(-12)+phi10*inf(-13)+phi11*inf(-14)+phi12*inf(-15)
                 - theta1*dedb6(-1) - theta2*dedb6(-2);
frml d22 dedb7 = -inf(-4)+phi1*inf(-5)+phi2*inf(-6)+phi3*inf(-7)+phi4*inf(-8)
                 +phi5*inf(-9)+phi6*inf(-10)+phi7*inf(-11)+phi8*inf(-12)
                 +phi9*inf(-13)+phi10*inf(-14)+phi11*inf(-15)+phi12*inf(-16)
                 - theta1*dedb7(-1) - theta2*dedb7(-2);

list deqs d1-d22;
list dvars dedp1-dedp12 dedt1-dedt2 deda dedb1-dedb7;
?
?  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
copy @smpl esmpl;
genr eqe;
mat ssrold = e'e;
print ssrold;
?
mat novar = nrow(b);
supres @logl @nob @coef @smpl;
const maxit,50 maxsqz,30 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 determine stepsize.

  mat relchg = abs(delt)/(abs(b) + 10*tol);
  mat worst = max(relchg);
  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 relchg 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;
yhat = fygm3 - e;
corr(silent) fygm3 yhat;
set rsq = @corr(2,1)**2;
print rsq;
smpl 88:1 88:6;
plot (device=char) fygm3 y yhat p;
end;
noprint;
load fygm3 fm1 ip pw;
 2.82 138.9  46.0  31.7
 2.70 139.4  46.9  31.7
 2.80 139.8  47.6  31.7
 2.95 139.7  48.6  31.8
 2.84 140.7  49.3  31.8
 3.21 141.2  49.4  31.7
 3.20 141.7  48.2  31.7
 3.38 141.9  46.6  31.6
 4.04 141.0  46.5  31.7
 4.05 140.5  46.2  31.6
 4.15 140.4  46.5  31.5
 4.49 140.0  49.3  31.5
 4.35 140.0  50.6  31.6
 3.96 139.9  50.2  31.6
 3.31 139.8  49.7  31.8
 3.23 139.6  49.3  31.8
 3.29 139.6  49.3  31.7
 2.46 139.6  48.7  31.7
 2.30 140.2  48.5  31.7
 2.30 141.3  48.4  31.6
 2.48 141.2  47.9  31.6
 2.30 141.0  47.9  31.7
 2.37 140.9  47.2  31.7
 2.25 140.7  46.3  31.7
 2.24 141.1  46.4  31.8
 2.42 141.6  46.3  31.8
 2.39 141.9  46.6  31.8
 2.29 142.2  47.5  31.6
 2.29 142.7  48.3  31.5
 2.33 142.9  48.9  31.3
 2.24 143.0  49.5  31.5
 2.39 143.5  50.0  31.5
 2.28 143.8  49.9  31.5
 2.30 144.2  50.9  31.5
 2.48 144.8  51.7  31.5
 2.60 145.2  52.1  31.6
 2.72 145.3  51.7  31.7
 2.73 145.7  52.5  31.7
 2.72 146.0  52.8  31.7
 2.73 146.4  52.9  31.6
 2.68 146.9  52.8  31.5
 2.73 146.6  52.7  31.5
 2.92 146.5  53.2  31.6
 2.82 146.6  53.3  31.6
 2.78 146.3  53.6  31.9
 2.74 146.8  53.7  31.7
 2.83 147.3  53.9  31.7
 2.87 147.9  53.9  31.6
 2.91 148.3  54.3  31.6
 2.92 148.9  54.9  31.5
 2.89 149.2  55.3  31.5
 2.90 149.7  55.8  31.4
 2.92 150.4  56.4  31.5
 2.99 150.5  56.6  31.6
 3.18 151.4  56.4  31.7
 3.32 151.8  56.5  31.6
 3.38 152.0  57.1  31.6
 3.45 152.6  57.5  31.6
 3.52 153.7  57.7  31.7
 3.52 153.4  57.6  31.6
 3.52 153.8  58.1  31.8
 3.53 154.3  58.5  31.6
 3.54 154.5  58.5  31.6
 3.47 154.8  59.5  31.6
 3.48 155.4  59.8  31.5
 3.48 155.7  60.0  31.5
 3.46 156.9  60.4  31.6
 3.50 157.9  60.8  31.6
 3.53 158.8  61.0  31.7
 3.57 159.3  60.2  31.7
 3.64 160.0  62.0  31.7
 3.84 160.4  62.7  31.7
 3.81 160.8  63.4  31.8
 3.93 161.0  63.8  31.9
 3.93 161.5  64.7  31.9
 3.93 162.1  64.9  32.0
 3.89 161.8  65.5  32.1
 3.80 162.3  66.0  32.4
 3.84 163.1  66.6  32.4
 3.84 163.7  66.9  32.4
 3.92 164.9  67.0  32.4
 4.03 166.0  67.7  32.5
 4.09 166.8  68.0  32.6
 4.38 167.9  68.8  32.8
 4.59 169.1  69.5  32.9
 4.65 169.7  70.0  33.2
 4.59 170.5  70.9  33.2
 4.62 171.9  71.0  33.2
 4.64 171.4  71.7  33.2
 4.50 171.6  72.0  33.3
 4.80 170.4  72.4  33.5
 4.96 170.9  72.5  33.6
 5.37 172.0  73.2  33.6
 5.35 171.2  73.7  33.4
 5.32 171.4  73.2  33.3
 4.96 172.1  73.3  33.3
 4.72 171.9  73.7  33.4
 4.56 173.0  72.8  33.4
 4.26 174.9  72.4  33.3
 3.84 174.3  73.1  33.1
 3.60 175.7  72.5  33.3
 3.54 177.1  72.5  33.5
 4.21 178.2  72.3  33.5
 4.27 179.8  73.7  33.4
 4.42 180.7  73.6  33.4
 4.56 181.7  74.2  33.4
 4.73 182.4  75.2  33.4
 4.97 183.3  76.0  33.7
 5.00 184.5  76.0  33.8
 4.98 184.8  76.2  34.0
 5.17 185.5  76.5  34.1
 5.38 186.7  76.6  34.1
 5.66 188.1  77.4  34.2
 5.52 189.5  77.7  34.2
 5.31 190.6  77.6  34.3
 5.09 191.9  77.8  34.2
 5.19 192.8  78.1  34.4
 5.35 194.1  78.3  34.4
 5.45 196.1  79.3  34.5
 5.96 197.5  79.5  34.6
 6.14 198.7  80.0  34.8
 6.12 199.4  80.5  35.0
 6.02 200.1  81.2  35.2
 6.11 200.8  80.9  35.3
 6.04 200.9  80.6  35.5
 6.44 201.4  81.3  35.7
 7.00 201.7  81.8  35.8
 6.98 201.8  82.0  35.7
 7.09 202.2  81.9  35.8
 7.00 203.0  82.0  35.9
 7.24 203.6  81.2  36.1
 7.82 204.0  81.0  36.3
 7.87 206.5  79.5  36.5
 7.13 205.1  79.4  36.7
 6.63 205.8  79.3  36.7
 6.51 206.7  79.1  36.8
 6.84 207.4  79.0  36.8
 6.68 207.6  78.8  36.9
 6.45 208.1  79.0  37.1
 6.41 210.0  78.8  36.9
 6.13 211.9  78.3  37.1
 5.91 212.9  76.7  37.1
 5.28 213.7  76.2  37.1
 4.87 214.5  78.0  37.1
 4.44 215.9  78.6  37.3
 3.70 217.5  78.4  37.7
 3.38 218.8  78.4  37.8
 3.86 220.1  78.8  37.9
 4.14 222.1  79.2  38.1
 4.75 223.5  79.5  38.2
 5.40 225.0  79.3  38.3
 4.94 225.7  78.8  38.5
 4.69 226.5  80.1  38.3
 4.46 227.3  80.7  38.3
 4.22 227.8  81.1  38.3
 4.01 228.4  82.0  38.6
 3.38 230.4  83.8  38.8
 3.20 232.4  84.4  39.2
 3.73 234.4  85.1  39.2
 3.71 235.6  86.5  39.3
 3.69 235.9  86.3  39.5
 3.91 236.8  86.5  39.7
 3.98 238.8  86.4  40.0
 4.02 240.9  87.6  40.1
 4.66 243.2  88.5  40.2
 4.74 245.0  89.8  40.1
 4.78 246.4  90.9  40.3
 5.07 249.4  91.8  41.1
 5.41 251.7  91.8  41.6
 5.60 252.2  93.1  42.4
 6.09 251.7  93.1  43.4
 6.26 252.7  93.4  43.6
 6.36 254.9  93.8  44.5
 7.19 256.9  94.5  45.5
 8.01 257.6  95.1  44.9
 8.67 257.9  95.1  47.5
 8.29 258.0  95.8  46.7
 7.22 259.1  96.1  46.3
 7.83 261.1  96.2  46.5
 7.45 263.0  94.7  47.4
 7.77 264.1  93.3  49.0
 7.12 265.4  93.0  50.0
 7.96 266.8  93.4  50.6
 8.33 267.1  93.2  51.0
 8.23 267.7  94.3  51.8
 7.90 268.6  94.6  52.0
 7.55 269.4  94.2  54.0
 8.96 270.2  93.9  55.9
 8.06 271.2  94.2  55.9
 7.46 272.4  93.6  56.9
 7.47 273.8  90.9  57.4
 7.15 274.4  87.1  57.3
 6.26 274.1  84.8  57.4
 5.50 274.8  83.5  57.2
 5.49 276.7  82.0  56.9
 5.61 276.1  82.7  57.5
 5.23 278.9  82.5  57.9
 5.34 282.7  83.6  58.0
 6.13 283.3  84.1  58.7
 6.44 284.8  85.6  59.0
 6.42 285.6  86.4  59.4
 5.96 285.2  86.9  59.8
 5.48 287.9  87.7  59.5
 5.44 287.6  88.4  59.7
 4.87 288.9  89.3  59.9
 4.88 291.1  90.9  59.9
 5.00 292.3  90.7  60.0
 4.86 294.2  91.1  60.6
 5.20 296.1  92.1  60.8
 5.41 295.9  92.2  61.2
 5.23 297.1  92.7  61.6
 5.14 299.0  93.2  61.4
 5.08 299.6  93.5  61.8
 4.92 303.0  93.9  61.9
 4.75 303.6  95.4  62.0
 4.35 306.5  96.2  62.5
 4.62 309.3  96.5  62.8
 4.67 311.6  97.2  63.5
 4.60 313.6  98.0  64.1
 4.54 316.1  99.0  64.9
 4.96 316.6  99.6  65.2
 5.02 318.2 100.4  65.0
 5.19 320.7 100.7  65.1
 5.49 322.2 101.0  65.0
 5.81 324.5 101.4  65.3
 6.16 327.5 101.8  65.6
 6.10 329.2 102.1  65.8
 6.07 331.4 102.1  66.2
 6.44 334.9 101.6  66.8
 6.45 335.4 101.6  67.5
 6.29 337.0 103.0  68.1
 6.29 340.4 105.5  69.0
 6.41 343.5 105.8  69.5
 6.73 345.8 106.9  70.0
 7.01 347.8 107.5  70.4
 7.08 349.4 107.7  70.4
 7.85 353.4 108.3  71.0
 7.99 354.4 109.2  71.8
 8.64 356.2 109.9  72.1
 9.08 358.7 110.8  72.7
 9.35 359.4 110.3  73.8
 9.32 361.0 110.9  74.9
 9.48 361.7 111.2  75.8
 9.46 364.8 109.9  76.9
 9.61 365.8 110.9  77.5
 9.06 371.2 110.9  78.0
 9.24 375.8 110.5  79.2
 9.52 379.8 110.2  79.6
10.26 384.1 110.4  80.9
11.70 381.8 111.0  82.1
11.79 384.2 111.0  82.6
12.04 386.1 111.0  83.4
12.00 386.2 111.3  85.2
12.86 390.5 111.4  86.9
15.20 387.7 111.4  87.5
13.20 379.5 109.1  87.8
 8.58 380.8 106.2  88.3
 7.07 386.6 105.0  88.7
 8.06 392.2 104.8  90.3
 9.13 401.5 106.3  91.5
10.27 409.1 107.7  91.7
11.62 410.4 108.5  92.8
13.73 415.5 110.7  93.2
15.49 412.2 111.0  93.8
15.02 411.7 111.0  95.2
14.79 415.5 111.2  96.1
13.36 417.7 111.6  97.0
13.69 422.7 110.6  98.0
16.30 421.6 111.2  98.3
14.73 422.0 112.0  98.5
14.95 425.5 113.4  99.0
15.51 429.6 112.8  99.0
14.70 432.1 111.5  98.8
13.54 429.4 110.4  98.9
10.86 434.3 109.0  98.8
10.85 439.1 107.4  98.8
12.28 443.3 105.4  99.7
13.48 442.1 107.0  99.8
12.68 441.2 105.8  99.6
12.70 443.3 104.5  99.6
12.09 444.4 103.6  99.8
12.47 445.6 103.0 100.0
11.35 447.4 102.5 100.4
 8.68 453.4 102.0 100.3
 7.92 460.9 101.3 100.0
 7.71 466.1 100.5 100.2
 8.07 473.1 100.6 100.3
 7.94 476.4 100.5 100.5
 7.86 477.3 102.5 100.2
 8.11 484.0 103.3 100.5
 8.35 489.0 104.2 100.4
 8.21 491.4 105.6 100.4
 8.19 498.2 106.9 100.8
 8.79 502.5 107.8 101.0
 9.08 508.5 109.8 101.3
 9.34 511.8 111.6 101.8
 9.00 515.4 113.7 102.0
 8.64 518.2 114.4 102.2
 8.76 520.0 114.8 102.1
 9.00 522.1 115.5 102.3
 8.90 524.7 118.5 102.9
 9.09 527.9 119.3 103.2
 9.52 531.3 119.9 103.9
 9.69 533.1 120.5 104.0
 9.83 535.8 121.0 104.1
 9.87 540.0 121.9 104.0
10.12 540.8 122.8 104.2
10.47 541.5 123.0 103.8
10.37 545.1 122.4 103.4
 9.74 543.6 122.1 103.4
 8.61 547.1 122.7 103.7
 8.06 551.9 122.7 103.5
 7.76 555.9 122.4 103.4
 8.27 563.0 122.9 103.3
 8.52 566.3 123.3 103.1
 7.95 569.8 123.1 103.3
 7.48 575.1 123.7 103.5
 6.95 583.2 123.5 103.3
 7.08 588.9 123.4 103.2
 7.14 596.9 124.1 102.7
 7.10 604.3 124.4 102.1
 7.16 607.2 123.7 102.9
 7.24 612.2 124.8 103.4
 7.10 620.1 125.4 103.6
 7.07 621.7 126.4 103.2
 7.06 625.2 125.5 101.7
 6.56 634.0 123.9 100.3
 6.06 641.2 124.7  99.6
 6.15 651.7 124.3 100.0
 6.21 661.3 124.1  99.9
 5.83 670.8 124.8  99.4
 5.53 680.5 124.9  99.3
 5.21 687.4 124.5  99.4
 5.18 694.9 125.3  99.7
 5.35 706.4 125.7  99.8
 5.53 725.4 126.8  99.7
 5.43 731.4 126.2 100.5
 5.59 731.3 127.1 101.0
 5.59 734.2 127.4 101.2
 5.64 744.7 127.4 101.9
 5.66 746.5 128.2 102.6
 5.67 742.1 129.1 103.0
 5.69 743.6 130.6 103.5
 6.04 746.5 131.2 103.8
 6.40 747.5 131.0 103.7
 6.13 756.2 132.5 104.1
 5.69 752.7 133.2 104.2
 5.77 750.8 133.9 104.2
 5.81 758.8 134.4 104.6
 5.66 759.5 134.4 104.8
 5.70 763.0 134.7 104.9
 5.91 770.0 135.4 105.8
 6.26 770.0 136.1 106.5
 6.46 776.2 136.6 107.4
; end;