options double crt;
? ML PROC example
? Regression model with ARMA(8,2) errors
? Follows Pindyck & Rubinfeld (1997) Section 19.6

freq m;
smpl 59:1 94:8;
load;
smpl 59:2 94:8;
gm2=(m2-m2(-1))/m2(-1);
gpw=(pw-pw(-1))/pw(-1);

? OLS estimate
smpl 60:1 94:8;
olsq r c ip gm2 gpw(-1);
form(varpref=b,resid) eq1;  ? save estimates as an equation in residual form
print eq1;
u=@res;

? ARIMA estimate
bjest(constant, nar=8, nma=2, nostart, nocumplo, noplot) u;

? Now combine the regression and ARMA into one estimation

? Save results from BJEST for starting values
unmake @coef phi1-phi8 theta1 theta2 bjconst;
set sigma = sqrt(@ssr/@nob);

list allpar b0 bip bgm2 bgpw1 phi1-phi8 theta1 theta2 sigma;
param allpar;
smpl 60:1 94:8;
supres smpl;
ML(maxit=100) olsarma allpar;  ? use ML Proc feature  (See Proc olsarma below)

Proc olsarma;
if sigma <= 0; then;
  set @logl = @miss;
else; do;
  smpl 59:1 94:8;
  e = 0;  ? zero presample values
  u = 0;
  smpl 60:1 94:8;
  genr eq1 u;  ? evaluate structural residuals
  ? evaluate filtered residuals
  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)
        - theta1*e(-1) - theta2*e(-2);
  logl = -log(sigma) + lnorm(e/sigma);  ? log likelihood
  mat @logl = sum(logl);
enddo;
endproc;
end;
noprint;
read r ip m2 pw;  ? originally from ex42.xls
4.436 39.6 298.2 31.6
3.954 39.2 298.4 31.6
3.439 38.9 299.4 31.8
3.244 38.6 300.0 31.8
3.392 38.5 300.9 31.7
2.641 38.1 302.3 31.7
2.396 37.9 304.1 31.7
2.286 37.9 306.9 31.6
2.489 37.5 308.4 31.6
2.426 37.4 309.5 31.7
2.384 36.9 310.9 31.7
2.272 36.2 312.4 31.7
2.302 36.3 314.1 31.8
2.408 36.2 316.5 31.8
2.420 36.4 318.3 31.8
2.327 37.2 319.9 31.6
2.288 37.7 322.2 31.5
2.359 38.3 324.3 31.3
2.268 38.7 325.6 31.5
2.402 39.1 327.6 31.5
2.304 39.0 329.5 31.5
2.350 39.8 331.1 31.5
2.458 40.4 333.4 31.5
2.617 40.7 335.5 31.6
2.746 40.4 337.5 31.7
2.752 41.1 340.1 31.7
2.719 41.3 343.1 31.7
2.735 41.4 345.5 31.6
2.694 41.3 347.4 31.5
2.719 41.2 349.3 31.5
2.945 41.6 350.8 31.6
2.837 41.7 352.8 31.6
2.792 41.9 354.9 31.9
2.751 42.0 357.2 31.7
2.803 42.2 359.8 31.7
2.856 42.2 362.7 31.6
2.914 42.5 365.2 31.6
2.916 42.9 367.9 31.5
2.897 43.2 370.7 31.5
2.909 43.6 373.3 31.4
2.920 44.1 376.0 31.5
2.995 44.3 378.4 31.6
3.143 44.1 381.1 31.7
3.320 44.2 383.6 31.6
3.379 44.6 386.0 31.6
3.453 44.9 388.3 31.6
3.522 45.1 391.5 31.7
3.523 45.1 393.3 31.6
3.529 45.5 395.2 31.8
3.532 45.8 397.6 31.6
3.553 45.8 399.8 31.6
3.484 46.5 401.7 31.6
3.482 46.8 404.2 31.5
3.478 46.9 407.1 31.5
3.479 47.2 410.1 31.6
3.506 47.5 413.4 31.6
3.527 47.7 416.9 31.7
3.575 47.0 419.1 31.7
3.624 48.5 422.0 31.7
3.856 49.1 424.8 31.7
3.828 49.6 427.5 31.8
3.929 49.9 430.4 31.9
3.942 50.6 433.2 31.9
3.932 50.8 435.4 32.0
3.895 51.2 437.2 32.1
3.810 51.6 440.1 32.4
3.831 52.1 442.9 32.4
3.836 52.3 445.8 32.4
3.912 52.4 449.5 32.4
4.032 52.9 452.6 32.5
4.082 53.2 455.7 32.6
4.362 53.8 459.2 32.8
4.596 54.4 462.0 32.9
4.670 54.7 464.6 33.2
4.626 55.5 467.2 33.2
4.611 55.5 469.3 33.2
4.642 56.1 470.1 33.2
4.539 56.3 471.2 33.3
4.855 56.6 470.8 33.5
4.932 56.7 472.6 33.6
5.356 57.2 475.4 33.6
5.387 57.6 475.7 33.4
5.344 57.2 477.3 33.3
5.007 57.3 480.2 33.3
4.759 57.6 481.6 33.4
4.554 57.0 485.1 33.4
4.288 56.6 489.7 33.3
3.852 57.2 492.1 33.1
3.640 56.7 497.2 33.3
3.480 56.7 502.0 33.5
4.308 56.5 506.3 33.5
4.275 57.6 510.8 33.4
4.451 57.5 514.7 33.4
4.588 58.0 518.2 33.4
4.762 58.8 521.2 33.4
5.012 59.5 524.8 33.7
5.081 59.4 527.1 33.8
4.969 59.6 530.4 34.0
5.144 59.8 533.2 34.1
5.365 59.9 535.7 34.1
5.621 60.6 538.9 34.2
5.544 60.8 542.6 34.2
5.382 60.7 545.6 34.3
5.095 60.9 549.4 34.2
5.202 61.1 553.5 34.4
5.334 61.2 557.6 34.4
5.492 62.0 562.4 34.5
5.916 62.2 566.9 34.6
6.177 62.6 569.3 34.8
6.156 63.0 571.9 35.0
6.080 63.5 574.4 35.2
6.150 63.2 575.7 35.3
6.077 63.0 576.5 35.5
6.493 63.6 578.5 35.7
7.004 63.9 579.5 35.8
7.007 64.1 580.1 35.7
7.129 64.1 582.1 35.8
7.040 64.1 583.4 35.9
7.193 63.5 585.4 36.1
7.720 63.3 587.9 36.3
7.914 62.1 589.6 36.5
7.164 62.1 586.4 36.7
6.710 62.0 587.3 36.7
6.480 61.9 588.4 36.8
7.035 61.8 591.5 36.8
6.742 61.6 595.2 36.9
6.468 61.7 599.1 37.1
6.412 61.6 604.9 36.9
6.244 61.2 611.2 37.1
5.927 60.0 616.4 37.1
5.288 59.6 621.1 37.1
4.860 61.0 626.6 37.1
4.494 61.5 633.0 37.3
3.773 61.3 641.0 37.7
3.323 61.3 649.9 37.8
3.780 61.6 658.5 37.9
4.139 61.9 666.8 38.1
4.699 62.2 673.0 38.2
5.405 62.0 679.6 38.3
5.078 61.7 685.6 38.5
4.668 62.7 692.5 38.3
4.489 63.1 698.4 38.3
4.191 63.4 704.6 38.3
4.023 64.1 710.3 38.6
3.403 65.6 717.7 38.8
3.180 66.0 725.7 39.2
3.723 66.5 733.5 39.2
3.723 67.6 738.4 39.3
3.648 67.5 743.3 39.5
3.874 67.7 749.7 39.7
4.059 67.6 759.4 40.0
4.014 68.5 768.7 40.1
4.651 69.2 778.3 40.2
4.719 70.2 786.9 40.1
4.774 71.1 793.9 40.3
5.061 71.7 802.3 41.1
5.307 71.8 810.3 41.6
5.558 72.8 814.1 42.4
6.054 72.8 815.3 43.4
6.289 73.0 819.7 43.6
6.348 73.4 826.8 44.5
7.188 73.9 833.2 45.5
8.015 74.4 836.5 44.9
8.672 74.3 838.8 47.5
8.478 74.9 839.3 46.7
7.155 75.2 842.6 46.3
7.866 75.2 848.9 46.5
7.364 74.0 855.5 47.4
7.755 73.0 859.7 49.0
7.060 72.7 864.2 50.0
7.986 73.0 870.1 50.6
8.229 72.9 873.0 51.0
8.430 73.8 874.6 51.8
8.145 74.0 877.8 52.0
7.752 73.6 881.5 54.0
8.744 73.4 884.1 55.9
8.363 73.7 888.2 55.9
7.244 73.2 893.6 56.9
7.585 71.1 898.9 57.4
7.179 68.1 902.5 57.3
6.493 66.3 906.5 57.4
5.583 65.3 914.1 57.2
5.544 64.1 925.6 56.9
5.694 64.7 935.5 57.5
5.315 64.5 947.8 57.9
5.193 65.3 963.4 58.0
6.164 65.7 975.1 58.7
6.463 66.9 983.9 59.0
6.383 67.6 991.8 59.4
6.081 67.9 997.9 59.8
5.468 68.6 1008.3 59.5
5.504 69.1 1017.0 59.7
4.961 69.9 1027.2 59.9
4.852 71.1 1041.0 59.9
5.047 70.9 1050.1 60.0
4.878 71.2 1060.8 60.6
5.185 72.0 1072.7 60.8
5.443 72.1 1077.7 61.2
5.278 72.5 1086.6 61.6
5.153 72.9 1099.1 61.4
5.075 73.1 1111.3 61.8
4.930 73.4 1126.3 61.9
4.810 74.6 1138.8 62.0
4.355 75.2 1152.7 62.5
4.597 75.5 1166.7 62.8
4.662 75.9 1178.2 63.5
4.613 76.6 1188.8 64.1
4.540 77.7 1200.2 64.9
4.942 78.3 1209.1 65.2
5.004 78.9 1217.7 65.0
5.146 78.9 1227.7 65.1
5.500 79.0 1237.6 65.0
5.770 79.4 1246.8 65.3
6.188 79.4 1255.7 65.6
6.160 79.5 1263.7 65.8
6.063 79.1 1271.5 66.2
6.448 78.8 1280.9 66.8
6.457 79.0 1286.3 67.5
6.319 80.0 1292.9 68.1
6.306 82.0 1301.2 69.0
6.430 82.3 1310.1 69.5
6.707 83.1 1318.1 70.0
7.074 83.3 1324.9 70.4
7.036 83.6 1334.0 70.4
7.836 84.1 1346.8 71.0
8.132 84.5 1354.3 71.8
8.787 85.2 1360.9 72.1
9.122 85.4 1368.0 72.7
9.351 85.1 1372.6 73.8
9.265 85.8 1378.8 74.9
9.457 86.1 1389.0 75.8
9.493 85.2 1402.6 76.9
9.579 86.2 1409.5 77.5
9.045 86.1 1423.3 78.0
9.262 85.6 1435.0 79.2
9.450 85.3 1447.3 79.6
10.182 85.5 1456.8 80.9
11.472 86.0 1462.4 82.1
11.868 85.7 1468.1 82.6
12.071 85.6 1475.7 83.4
12.036 85.9 1483.7 85.2
12.814 86.2 1495.4 86.9
15.526 86.2 1501.8 87.5
14.003 84.5 1502.9 87.8
9.15 82.5 1511.8 88.3
6.995 81.5 1529.6 88.7
8.126 81.2 1545.7 90.3
9.259 82.4 1563.4 91.5
10.321 83.5 1575.9 91.7
11.58 84.0 1587.2 92.8
13.888 85.5 1599.2 93.2
15.661 85.9 1601.0 93.8
14.724 85.2 1608.3 95.2
14.905 85.4 1619.7 96.1
13.478 85.7 1638.1 97.0
13.635 85.0 1660.0 98.0
16.295 85.6 1665.0 98.3
14.557 86.1 1670.7 98.5
14.699 87.1 1682.4 99.0
15.612 86.9 1696.3 99.0
14.951 86.5 1708.3 98.8
13.873 85.8 1724.2 98.9
11.269 84.8 1738.5 98.8
10.926 84.1 1756.0 98.8
12.412 82.4 1772.5 99.7
13.78 84.2 1775.6 99.8
12.493 83.7 1787.7 99.6
12.821 83.2 1805.0 99.6
12.148 82.7 1816.7 99.8
12.108 82.4 1827.1 100.0
11.914 82.0 1835.5 100.4
9.006 81.6 1851.3 100.3
8.196 81.0 1865.5 100.0
7.75 80.3 1877.8 100.2
8.042 80.0 1890.4 100.3
8.013 79.3 1910.9 100.5
7.81 80.8 1965.6 100.2
8.13 80.7 2002.0 100.5
8.304 81.3 2020.0 100.4
8.252 82.3 2034.2 100.4
8.185 83.2 2048.1 100.8
8.82 83.7 2058.1 101.0
9.12 85.3 2070.6 101.3
9.39 86.5 2079.1 101.8
9.05 87.9 2088.3 102.0
8.71 88.6 2105.4 102.2
8.71 88.8 2118.0 102.1
8.96 89.2 2127.9 102.3
8.93 91.0 2143.5 102.9
9.03 90.9 2163.5 103.2
9.44 91.9 2180.0 103.9
9.69 92.4 2196.0 104.0
9.9 93.0 2209.2 104.1
9.94 93.5 2220.6 104.0
10.13 93.9 2229.1 104.2
10.49 94.0 2235.8 103.8
10.41 93.9 2251.0 103.4
9.97 93.2 2264.7 103.4
8.79 93.3 2287.2 103.7
8.16 92.8 2312.4 103.5
7.76 93.1 2337.6 103.4
8.22 93.8 2359.4 103.3
8.57 94.1 2371.8 103.1
8.0 94.5 2381.0 103.3
7.56 94.7 2395.5 103.5
7.01 94.4 2419.7 103.3
7.05 94.1 2435.6 103.2
7.18 94.5 2450.2 102.7
7.08 95.0 2463.2 102.1
7.17 94.2 2474.0 102.9
7.2 94.6 2484.1 103.4
7.07 95.6 2497.8 103.6
7.04 96.1 2507.6 103.2
7.03 95.5 2518.8 101.7
6.59 94.6 2539.4 100.3
6.06 94.8 2564.3 99.6
6.12 94.7 2591.4 100.0
6.21 94.3 2612.0 99.9
5.84 94.8 2633.1 99.4
5.57 94.9 2654.1 99.3
5.19 95.0 2674.7 99.4
5.18 95.6 2694.9 99.7
5.35 96.3 2709.5 99.8
5.49 96.8 2734.6 99.7
5.45 96.507 2750.6 100.5
5.59 97.885 2754.6 101.0
5.56 98.249 2760.0 101.2
5.76 98.774 2772.7 101.9
5.75 99.396 2779.7 102.6
5.69 100.251 2781.0 103.0
5.78 100.616 2786.1 103.5
6.0 100.92 2796.1 103.8
6.32 100.716 2806.5 103.7
6.4 102.052 2821.9 104.1
5.81 102.158 2827.0 104.2
5.8 102.825 2834.4 104.2
5.9 103.157 2857.1 104.6
5.69 103.389 2879.4 104.8
5.69 103.401 2899.1 104.9
5.92 104.254 2919.9 105.8
6.27 103.982 2934.5 106.5
6.5 104.012 2946.6 107.2
6.73 104.61 2957.3 107.9
7.02 105.206 2961.1 108.0
7.23 104.684 2965.9 108.1
7.34 104.994 2975.9 108.2
7.68 105.599 2989.9 108.3
8.09 106.271 2997.9 109.0
8.29 106.641 3001.4 110.5
8.48 106.157 3002.3 110.8
8.83 107.072 3009.4 111.5
8.7 107.071 3016.8 112.3
8.4 106.702 3021.8 113.2
8.22 106.36 3037.4 112.9
7.92 105.306 3062.7 112.8
7.91 105.845 3084.1 112.0
7.72 105.376 3103.1 112.4
7.59 104.988 3125.0 112.8
7.67 105.357 3144.0 112.7
7.64 106.06 3164.0 113.0
7.64 105.519 3176.0 114.9
7.76 106.091 3188.1 114.4
7.87 106.423 3199.8 114.2
7.78 105.722 3212.8 114.1
7.78 106.479 3211.0 114.6
7.74 106.669 3225.1 114.3
7.66 106.492 3234.0 114.5
7.44 106.798 3251.9 116.5
7.38 106.815 3266.1 118.4
7.19 106.322 3268.9 120.8
7.07 104.967 3272.6 120.1
6.81 104.538 3282.2 118.7
6.3 103.977 3296.2 119.0
5.95 102.919 3313.9 117.2
5.91 102.082 3332.2 116.2
5.67 102.376 3340.9 116.0
5.51 103.168 3350.2 116.5
5.6 104.315 3361.9 116.4
5.58 104.502 3364.0 116.1
5.39 104.767 3363.2 116.2
5.25 105.656 3362.9 116.1
5.03 105.76 3367.0 116.4
4.6 105.616 3375.9 116.4
4.12 105.088 3383.7 115.9
3.84 104.953 3391.9 115.6
3.84 105.63 3411.7 116.0
4.05 106.548 3414.9 116.1
3.81 107.264 3412.9 116.3
3.66 107.799 3411.8 117.2
3.7 107.507 3405.6 118.0
3.28 108.41 3406.2 117.9
3.14 108.205 3413.1 117.7
2.97 108.419 3421.8 118.0
2.84 109.152 3435.4 118.1
3.14 109.813 3439.2 117.8
3.25 110.01 3438.7 117.6
3.06 110.354 3436.6 118.0
2.95 110.807 3429.4 118.4
2.97 110.844 3427.5 118.7
2.89 111.095 3430.9 119.3
2.96 110.575 3454.6 119.7
3.1 110.765 3459.6 119.5
3.05 111.401 3459.1 119.2
3.05 111.424 3463.3 118.7
2.96 112.212 3469.9 118.7
3.04 112.297 3475.6 119.1
3.12 113.088 3487.0 119.0
3.08 114.142 3494.1 118.6
3.02 114.575 3499.0 119.1
3.21 115.471 3500.7 119.3
3.52 116.436 3506.5 119.7
3.74 116.839 3513.5 119.7
4.19 117.456 3511.6 119.9
4.18 118.091 3500.6 120.5
4.39 118.362 3508.0 120.7
4.5 118.93 3504.1 121.2
4.64 119.063 3503.8 121.0
4.96 119.894 3503.9 120.9
5.25 120.534 3506.8 121.5
5.64 121.484 3509.4 121.9
5.81 121.816 3514.2 122.9
5.8 121.72 3514.1 123.5
5.73 121.888 3519.1 123.9
5.67 121.388 3529.2 124.6
5.7 121.339 3543.5 124.9
5.5 121.4 3574.0 125.3
5.47 121.5 3592.8 125.3
5.41 122.7 3612.7 125.1