Time Series Documentation Examples
/****************************************************************/
/* S A S S A M P L E L I B R A R Y */
/* */
/* NAME: TIMSEX */
/* TITLE: Time Series Documentation Examples */
/* PRODUCT: IML */
/* SYSTEM: ALL */
/* KEYS: */
/* PROCS: */
/* DATA: */
/* */
/* SUPPORT: GJW UPDATE: APRIL 1996 */
/* REF: */
/* MISC: */
/****************************************************************/
title 'Time Series Subroutine Documentation';
title2 'Minimum AIC Model Selection';
proc iml;
y = { 2.430 2.506 2.767 2.940 3.169 3.450 3.594 3.774 3.695 3.411
2.718 1.991 2.265 2.446 2.612 3.359 3.429 3.533 3.261 2.612
2.179 1.653 1.832 2.328 2.737 3.014 3.328 3.404 2.981 2.557
2.576 2.352 2.556 2.864 3.214 3.435 3.458 3.326 2.835 2.476
2.373 2.389 2.742 3.210 3.520 3.828 3.628 2.837 2.406 2.675
2.554 2.894 3.202 3.224 3.352 3.154 2.878 2.476 2.303 2.360
2.671 2.867 3.310 3.449 3.646 3.400 2.590 1.863 1.581 1.690
1.771 2.274 2.576 3.111 3.605 3.543 2.769 2.021 2.185 2.588
2.880 3.115 3.540 3.845 3.800 3.579 3.264 2.538 2.582 2.907
3.142 3.433 3.580 3.490 3.475 3.579 2.829 1.909 1.903 2.033
2.360 2.601 3.054 3.386 3.553 3.468 3.187 2.723 2.686 2.821
3.000 3.201 3.424 3.531 };
call tsunimar(arcoef,ev,nar,aic) data=y opt={-1 1} print=1
maxlag=20;
call tsunimar(arcoef,ev,nar,aic,y,20,{-1 1},,1);
call tsunimar(arcoef,ev,nar,aic,y,10,{-1 0},,1);
data one;
input invest income consum @@;
cards;
180 451 415 179 465 421 185 485 434 192 493 448
211 509 459 202 520 458 207 521 479 214 540 487
231 548 497 229 558 510 234 574 516 237 583 525
206 591 529 250 599 538 259 610 546 263 627 555
264 642 574 280 653 574 282 660 586 292 694 602
286 709 617 302 734 639 304 751 653 307 763 668
317 766 679 314 779 686 306 808 697 304 785 688
292 794 704 275 799 699 273 799 709 301 812 715
280 837 724 289 853 746 303 876 758 322 897 779
315 922 798 339 949 816 364 979 837 371 988 858
375 1025 881 432 1063 905 453 1104 934 460 1131 968
475 1137 983 496 1178 1013 494 1211 1034 498 1256 1064
526 1290 1101 519 1314 1102 516 1346 1145 531 1385 1173
573 1416 1216 551 1436 1229 538 1462 1242 532 1493 1267
558 1516 1295 524 1557 1317 525 1613 1355 519 1642 1371
526 1690 1402 510 1759 1452 519 1756 1485 538 1780 1516
549 1807 1549 570 1831 1567 559 1873 1588 584 1897 1631
611 1910 1650 597 1943 1685 603 1976 1722 619 2018 1752
635 2040 1774 658 2070 1807 675 2121 1831 700 2132 1842
692 2199 1890 759 2253 1958 782 2276 1948 816 2318 1994
844 2369 2061 830 2423 2056 853 2457 2102 852 2470 2121
833 2521 2145 860 2545 2164 870 2580 2206 830 2620 2225
801 2639 2235 824 2618 2237 831 2628 2250 830 2651 2271
;
proc iml;
use one;
read all into y var{invest income consum};
mdel = 1;
maice = 2;
misw = 0; /* instantaneous modeling ? */
opt = mdel || maice || misw;
maxlag = 10;
miss = 0;
print = 1;
call tsmulmar(arcoef,ev,nar,aic,y,maxlag,opt,miss,print);
call tsmulmar(arcoef,ev,nar,aic) data=y maxlag=5
opt={1 1 0} print=1;
call tsmulmar(arcoef,ev,nar,aic) data=y maxlag=3
opt={1 0 0} ;
print aic nar;
print arcoef;
call tsmulmar(arcoef,ev,nar,aic) data=y maxlag=3
opt={1 2 0};
print aic nar;
print arcoef;
title2 'Nonstationary Data Analysis';
data one;
input y @@;
cards;
.21232e1 .47451 -.171e-2 -.84434 -.10876e1
-.84429 -.15320e1 -.21097e1 -.28282e1 -.30424e1
-.31714e1 -.25042e1 -.40406e1 -.37741e1 -.24557e1
-.14803e1 -.11456e1 -.19861e1 -.24899e1 -.10926e1
.76909 .44457 -.98272 -.60115 -.51100e-2
-.75129 .14737 .25100e1 .28413e1 .22882
-.14294e1 -.22658e1 -.20462e1 -.17189e1 .31475
.49432e1 .74404e1 .60316e1 .44300e1 .25392e1
.88116 .99908 .20893e1 .14615e1 -.15465e1
-.39071e1 -.41050e1 -.45899e1 -.36374e1 -.25623e1
-.28320e1 -.22083e1 -.12521e1 -.60346 .15296e1
.27190e1 .22839e1 .21644e1 .22284e1 .18323e1
.10191e1 .53627 .14400e1 .27485e1 .23344e1
.29678e1 .44569e1 .44449e1 .47612e1 .57645e1
.48988e1 .24701e1 .30355e1 .45397e1 .25237e1
.85361 .37475 .61676 .38774 .24211e1
.50219e1 .59801e1 .51236e1 .41791e1 .32537e1
.74290e-1 -.90402 .11527e1 .19298 -.38438e1
-.52842e1 -.44210e1 -.42358e1 -.35756e1 -.68584
.22025e1 .67884 -.51910e-1 -.26841 -.14454e1
-.27263e1 -.10642e1 -.22906 .14353e1 .44310e1
.56587e1 .57044e1 .49740e1 .35969e1 .32536e1
.15313e1 -.54363 .17246e1 .22281e1 .11698e1
.31331e1 .37619e1 .18702e1 -.63447 -.16734e1
-.78362 .18155 .81437 .29880e1 .42316e1
.27936e1 .14584e1 .69219 .92169 .50336
-.14576 .28626 -.21177 -.18325 .83773
.21403e1 .32151e1 .39073e1 .17564e1 -.40430e-1
-.14468e1 -.30978e1 -.45090e1 -.34477e1 -.11195e1
.69229 -.44579 -.81135 .16924e1 .16261e1
-.40439 .44632 .25005e1 .10500e1 .18656e1
.29493e1 .38990e-1 -.21080e1 -.23002e1 -.51056e1
-.70257e1 -.67368e1 -.71630e1 -.67029e1 -.35206e1
-.91048 -.14017 .21923e1 .41561e1 .35830e1
.11135e1 .10722e1 .56274 -.60720e-1 .10540e1
.14742e1 .87608 -.50290e-1 -.46292 -.10444e1
-.15323e1 -.19734e1 -.19980e1 -.14040e1 -.98567
-.13120e1 -.20757e1 -.89996 -.10235e1 -.86877
-.58291 -.16572 .28356 -.13699e1 -.20766e1
-.25061e1 -.34979e1 -.30414e1 -.22379e1 -.14656e1
.16544e1 .27433e1 .18284e1 .19546e1 .17829e1
.28038e1 .14874e1 -.18358 -.20454e1 -.51580e1
-.59216e1 -.42272e1 -.31347e1 -.11411e1 .74276
.69111 .17371 .30344 -.96847 -.11461e1
.73357 .19426e1 .40275e1 .56222e1 .60117e1
.64635e1 .57200e1 .31722e1 .14605e1 -.14047e1
-.33388e1 -.19739e1 .75048 .37720e1 .57080e1
.56570e1 .27987e1 -.26068 -.10693e1 -.12593e1
-.91699 .16950e1 .33184e1 .37526e1 .28199e1
.52852 .44112 .18226 .43381 .16512e1
.19047e1 .41794 -.74695 -.12674e1 -.11783e1
-.23962 -.36487 -.10150e1 -.25589e1 -.32584e1
-.16839e1 -.20363e1 -.33336e1 -.38013e1 -.48810e1
-.70115e1 -.66677e1 -.53179e1 -.39982e1 -.27593e1
-.76430 .61031 .16508e1 .27397e1 .21227e1
.82413 .17823e1 .31185e1 .10319e1 .44284
.20106e1 -.29711 -.17797e1 -.26535e1 -.44488e1
-.49930e1 -.13722e1 .28765e1 .40531e1 .41888e1
.37341e1 .10123e1 -.48490e-1 .11352e1 .13888e1
.10163e1 .13922e1 .10181e1 -.12706e1 .49050e-1
.28326e1 .26521e1 .36238e1 .47693e1 .99788
-.37782e1 -.55912e1 -.57962e1 -.47187e1 -.82419
.30362e1 .38098e1 .34193e1 .30633e1 .10207
-.13569e1 -.57315 .17041 -.13010 .46305
.57370e-1 -.89257 -.69259 .41210e-1 .10538e1
.28650e1 .31371e1 .17423e1 .33408e1 .35503e1
.17936e1 .18962e1 .37921e1 .40597e1 .21531e1
.11832e1 .20175 -.17523 .45884 -.33998
-.34732 .70966 .28029 -.81689 -.17065e1
-.23841e1 -.45573e1 -.43359e1 -.39757e1 -.28036e1
-.72917 -.21099 -.33812 .38755 .73656
.15580e-1 .29561 .24164e1 .27155e1 .22664e1
.25401e1 .29552e1 .16478e1 .67895 .15853e1
-.20539 -.22975e1 -.15602e1 .16891 .87486
.58779 .13468e1 .48464 -.10825e1 -.19219e1
-.32107e1 -.45300e1 -.19356e1 .86894 .32397
-.78359 -.70134 -.25998e1 -.44587e1 -.13451e1
.24063e1 .39978e1 .66603e1 .52073e1 .10280e-1
-.29285e1 -.42959e1 -.53644e1 -.29264e1 .16018e1
.25112e1 .30417e1 .40855e1 .20552e1 -.91705
-.17546e1 -.23059e1 -.28742e1 -.24611e1 -.19649e1
-.29445e1 -.49109e1 -.66890e1 -.60487e1 -.40107e1
-.27389e1 -.25226e1 -.16680e1 -.12292 .15090e1
.13531e1 .96067 .65678 -.14941 .40654
.11915e1 .12979e1 .27594e1 .38072e1 .82062
-.14616 .56445 -.15341e1 -.29392e1 -.34430e-1
.13394e1 -.34905 .96274 .18512e1 -.19664
-.18437e1 -.63209 -.12943e1 -.23742e1 -.44357
-.38785 -.28229e1 -.12464e1 .20253e1 .24906e1
.14951e1 .31615e1 .14374e1 -.20224e1 -.17221e1
-.93806 -.23118e1 -.20556e1 -.89757 -.12143e1
-.20192e1 -.55518 -.98174 -.90652 .15837e1
.10687e1 .14387e1 .43464e1 .50423e1 .30744e1
.41017e1 .15820e1 -.19788e1 -.14845e1 -.72114
-.17572e1 -.78170e-1 .38380e-1 -.19383e1 -.11083e1
.20812e1 .23072e1 .19481e1 .23170e1 .23319
-.15642e1 -.25626e1 -.25176e1 -.38839e1 -.49541e1
-.35618e1 -.25752e1 -.17620e1 -.13164e1 -.14521e1
-.15164e1 -.12435e1 -.33419 .10726e1 .31957
-.17817 -.44265 -.17533e1 -.27862e1 -.73801
.19937e1 .27335 -.44323 .61213 -.96147
-.24286e1 .10454e1 .49832e1 .58430e1 .67043e1
.49056e1 -.11115 -.42396e1 -.45509e1 -.28420e1
-.33752 .11703e1 .20529e1 .14217e1 .71480e-1
-.16108 -.10602e1 -.26509 .29849e1 .23934e1
-.76810e-1 .24055 .54719 .36336 .44682e1
.74858e1 .56569e1 .37605e1 .40142e1 .17751e1
-.79662 -.19207e1 -.26013e1 -.34211e1 -.22944e1
-.96203 -.12799e1 -.14749e1 -.24096e1 -.31221e1
-.27273e1 -.28865e1 -.29953e1 -.12526e1 .10931e1
.25173e1 .18346e1 .28224 .18124 .31400e-1
.20074e1 .40952e1 .30277e1 .14903e1 .70693
-.23821e1 -.25325e1 -.20123e1 -.41759e1 -.41776e1
-.97520e-1 .24124e1 .22578e1 .33899e1 .34843e1
.73408 -.89786 .63628 .76202 .58840e-1
.13951e1 -.32835 -.51255e1 -.63345e1 -.40460e1
-.33949e1 -.13638e1 .19268e1 .19616e1 -.91085
-.16167e1 -.28469e1 -.47148e1 -.48544e1 -.31744e1
-.15196e1 -.78010e-1 .20722e1 .35228e1 .41356e1
.36124e1 .51169 -.39315e1 -.48369e1 -.27785e1
-.33760 .26125e1 .39145e1 .13366e1 -.38579e1
-.69886e1 -.75886e1 -.39628e1 -.42750e-1 .31792e1
.27930e1 .18711e1 -.44628 -.18752e1 -.23678e1
-.22431e1 .63020 .32844e1 .35382e1 .41680e1
.56101e1 .35509e1 .21272e1 .13487e1 -.71070e-1
.13370e-1 .99203 -.19809 -.25806e1 -.26215e1
-.14092e1 -.10503e1 -.11943e1 -.92094 -.10811e1
-.32402e1 -.49259e1 -.40744e1 -.49960e1 -.41957e1
-.22334e1 -.32103e1 -.55951e1 -.58428e1 -.50155e1
-.27862e1 -.41900e-2 .38169 -.78261 -.10571e1
-.50592 -.20864 .22935e1 .45191e1 .31465e1
.85198 -.95016 -.22236e1 -.20255e1 .13620e-1
.24389e1 .16594e1 -.74627 -.18741e1 -.23120e1
-.26552e1 -.18580e1 -.20596 .68591 .26157
-.20700 -.76957 .52308 .24229e1 .36764e1
.21684e1 .53821 .10316e1 .10136e1 .13441
.12428e1 .18857e1 .10108 -.70357 .29082
-.18591 -.10524e1 -.12246e1 -.78411 -.10854e1
-.10594e1 -.14190e1 -.25085e1 -.31476e1 -.49120
.32557e1 .53657e1 .60382e1 .50940e1 .21251e1
-.21401e1 -.45844e1 -.37850e1 -.21558e1 -.11368e1
.19739e1 .47841e1 .64890e1 .65086e1 .44846e1
.10576e1 -.31490e1 -.57643e1 -.51850e1 -.12196e1
.27302e1 .44350e1 .48051e1 .27548e1 -.13549e1
-.64529e1 -.73481e1 -.50199e1 -.31592e1 .14520e1
.48652e1 .34957e1 .21484e1 .12023e1 .38030
.93560 .37393e1 .39898e1 .18933e1 -.18009
-.22540e1 -.43827e1 -.46953e1 -.28134e1 -.95769
.87180e-1 .18364e1 .19586e1 -.13363e1 -.35681e1
-.26424e1 -.17582e1 -.34898 .28429e1 .48649e1
.26546e1 -.68844 -.26299e1 -.50732e1 -.58248e1
-.35492e1 -.13342e1 -.11452e1 -.10793 .14729e1
.50836 .32454 .28779e1 .48740e1 .35516e1
.44744e1 .35415e1 -.30018 -.73467e1 -.80053e1
-.76780e1 -.40052e1 .22489e1 .61895e1 .80277e1
.71266e1 .32113e1 -.24635e1 -.67759e1 -.77120e1
-.51839e1 -.12510e1 .26397e1 .56783e1 .51853e1
.87452 -.26642e1 -.28083e1 -.27995e1 -.11743e1
.51120 -.61972 -.28518e1 -.31683e1 -.23815e1
-.80850 .20733e1 .44195e1 .41069e1 .22232e1
.35531 -.28055e1 -.38599e1 -.20310e1 -.75040
.11734 .27131e1 .28551e1 .13469e1 .17174e1
.33616e1 .37837e1 .50780e1 .37710e1 .72495
-.77142 -.79002 .92667 .23868e1 .44050e1
.61124e1 .44085e1 .31815e1 .99798 -.18387e1
-.30464e1 -.32050e1 -.45968e1 -.42617e1 -.14815e1
-.19642 .15521 .14765e1 .31298e1 .21396e1
.12621 .66210 .23339e1 .14315e1 .18642e1
.22715e1 -.30368e1 -.67664e1 -.77819e1 -.91200e1
-.79972e1 -.33746e1 -.17698e1 -.31900e-2 -.18810e-1
-.27065e1 -.53475e1 -.50109e1 -.40961e1 -.37508e1
-.20028e1 -.11467 -.70140 -.12557e1 .53770
.10623e1 .12848e1 .17672e1 .20020e1 .21832e1
.26821e1 .30058e1 .35388e1 .43613e1 .32381e1
-.11110e1 -.50051e1 -.60840e1 -.44107e1 -.11380e1
.24261e1 .73555e1 .88091e1 .47620e1 .16492e1
-.47100 -.32299e1 -.33735e1 .40121 .45407e1
.67417e1 .87958e1 .74124e1 .23042e1 -.30663e1
-.67998e1 -.99142e1 -.91043e1 -.54271e1 -.27894e1
-.64066 -.15821 -.22627 .35440e-1 .10151
.35576 .12378e1 .69906 -.23062 -.20765e1
-.26094e1 -.27639e1 -.41822e1 -.43207e1 -.27278e1
-.22371e1 -.95365 .96700 .29827e1 .45331e1
.56392e1 .71368e1 .52588e1 .14579e1 -.15655e1
-.42760e1 -.61568e1 -.47034e1 -.15898e1 .78518
.17392e1 .21600e1 .11484e1 -.98559 -.16395e1
-.21925e1 -.26096e1 -.18653e1 -.10710e-1 .96932
.82964 .19314e1 .13027e1 -.19428e1 -.37536e1
-.61020e1 -.85213e1 -.66229e1 -.27024e1 -.17156e1
-.32903 .55055 -.21043 -.12342e1 -.19926e1
-.33864 -.34073e1 -.15925e1 .11302 .14315e1
.18899e1 .17847e1 .11641e1 -.66153 -.57238
-.82557 -.17608e1 -.23833e1 -.19450e1 -.16931e1
-.31799 .30429e1 .73039e1 .90978e1 .77165e1
.49446 .12464e1 -.31597e1 -.46957e1 -.31438e1
-.44870e-1 .37553e1 .71687e1 .72806e1 .30138e1
-.10553e1 -.20069e1 -.21633e1 -.62533 .24722e1
.61732e1 .68225e1 .36901e1 .22859 -.28079e1
-.39519e1 -.40152e1 -.23398e1 -.28602 .25187e1
.45845e1 .48295e1 .29352e1 -.14695e1 -.66874e1
;
proc iml;
use one;
read all var{y};
mdel = -1;
lspan = 300; /* local span of data */
maice = 1;
opt = mdel || lspan || maice;
call tsmlocar(arcoef,ev,nar,aic,first,last)
data=y maxlag=10 opt=opt print=2;
proc iml;
rudder = {
515 553 544 512 583 544 512 514
609 648 712 686 704 736 704 713
750 772 774 801 782 803 780 773
736 803 768 783 803 768 771 768
774 804 780 780 806 768 768 771
768 776 832 819 769 798 784 804
778 780 656 467 408 364 273 256
291 320 294 296 278 259 225 278
288 291 309 275 246 278 272 288
303 298 301 270 272 274 256 296
313 271 241 400 542 589 584 679
647 653 710 681 704 707 744 654
681 672 679 680 712 680 680 677
708 675 710 715 676 677 704 708
736 813 866 896 876 900 896 899
960 906 864 896 868 875 930 910
905 927 808 952 916 947 913 894
950 900 944 886 914 912 928 816
900 896 928 849 916 800 768 772
630 488 394 360 384 403 408 352
391 353 386 389 398 391 344 374
372 424 390 332 324 384 367 326
300 228 264 260 236 232 258 256
192 236 256 261 236 224 256 230
259 256 239 256 256 259 230 231
268 263 264 384 484 618 649 679
673 672 707 716 738 696 697 660
746 748 740 768 690 726 696 732
760 740 729 734 728 712 697 768
742 696 768 732 704 752 743 723
742 680 740 729 740 720 736 743
768 718 720 708 711 706 711 736
736 704 682 704 647 590 481 418
390 331 328 323 330 357 362 397
357 359 324 330 352 416 359 329
320 384 326 355 384 357 384 388
360 296 299 364 358 353 352 363
294 355 352 304 291 161 159 80
122 123 72 139 118 116 124 107
102 82 95 148 140 103 114 114
120 104 168 116 128 112 81 86
80 127 113 136 112 96 115 100
102 124 131 144 143 142 200 228
192 258 416 544 621 676 716 704
711 744 776 744 768 743 718 705
712 779 808 740 778 740 676 776
742 749 711 710 718 736 768 769
783 768 740 674 679 682 653 692
697 752 683 704 712 688 678 712
727 707 694 582 482 472 435 484
368 299 256 195 44 27 40 40
84 26 -3 20 -13 30 0 15
48 39 15 -16 3 -24 29 31
48 11 64 172 199 224 225 200
204 227 256 256 224 228 195 197
226 257 228 232 204 226 166 229
258 224 195 204 256 232 256 233
192 232 232 230 238 226 192 128
109 98 102 32 43 90 137 78
69 74 24 96 79 68 58 57
73 75 91 116 66 64 101 122
88 96 148 257 438 499 476 470
423 396 392 530 576 567 626 691
723 686 668 695 704 656 644 618
646 617 645 608 579 488 448 396
361 384 416 492 552 584 617 608
640 618 615 614 618 610 612 620
616 615 648 652 619 613 612 616
615 619 616 640 654 649 614 623
613 613 605 620 692 728 749 762
736 768 724 750 752 751 738 773
720 732 779 728 725 768 652 555
599 624 698 669 724 722 711 656
590 535 515 557 555 524 588 568
568 598 569 472 304 160 64 0
0 15 -29 34 128 192 172 230
206 165 108 138 101 96 195 200
228 234 265 288 264 320 320 271
226 256 262 269 231 296 263 267
256 290 335 454 523 548 608 570
648 544 358 344 301 388 422 461
442 421 410 385 392 407 482 486
496 561 528 567 550 572 546 592
607 480 448 395 384 382 392 389
360 363 364 370 377 408 482 452
498 512 483 525 494 524 515 548
524 517 512 514 520 448 513 494
512 544 525 522 513 512 512 488
491 520 514 488 488 460 480 484
516 514 513 524 578 512 519 526
554 524 518 493 483 512 519 480
458 503 512 517 512 512 512 549
548 528 564 544 506 512 528 538
527 490 513 531 512 514 562 555
568 592 607 612 592 613 556 542
553 548 576 528 544 520 530 512
545 480 522 512 521 576 545 576
554 521 490 424 399 389 324 225
199 168 140 160 0 131 161 192
164 203 225 164 166 164 163 201
195 202 193 192 232 324 331 357
362 330 368 376 372 342 352 366
352 367 384 421 402 408 421 466
440 448 429 416 416 424 472 454
485 419 332 347 316 416 442 496
466 393 380 406 432 356 398 425
448 473 486 490 553 548 552 423
260 256 195 289 388 454 426 416
298 321 387 328 421 416 418 461
416 327 258 195 237 262 360 397
480 481 484 458 427 454 384 292
399 392 384 389 459 458 521 -183};
yawing = {
-96 -56 -57 -61 8 -20 0 -32
6 -56 2 -60 -20 34 2 1
0 -54 -32 32 6 74 64 32
-50 0 -64 -90 -30 -24 -32 0
-32 -32 -57 -96 -28 -32 -64 -52
-62 -86 -56 -23 -80 -14 -119 -32
-88 -96 -105 -96 -159 -96 -83 -112
-94 -112 -155 -148 -112 -103 -140 -114
-150 -149 -143 -101 -83 -53 -60 -48
-58 -57 -20 -38 -51 -57 -126 -83
-31 22 16 44 59 -32 -96 -19
4 0 40 9 2 0 72 6
33 9 14 5 2 8 32 14
66 43 36 8 8 72 104 136
64 8 38 64 46 44 3 45
78 43 96 68 1 -23 32 15
96 97 40 115 89 154 84 -8
53 0 106 65 99 64 52 -25
16 18 10 -28 -28 -27 -94 -77
-112 -96 -74 -124 -83 -55 -64 -80
-60 -125 -176 -131 -116 -128 -148 -96
-84 -33 -80 -89 -126 -150 -150 -188
-150 -128 -85 -89 -90 -59 -20 -95
-160 -160 -160 -160 -125 -96 -53 -64
-88 -92 -96 -93 -64 -64 -84 -56
-32 4 13 8 2 5 -32 -20
-24 8 1 64 67 56 34 32
97 73 31 17 -32 15 26 48
96 51 3 10 16 0 -104 -9
-16 -36 41 40 14 -2 -48 -48
26 -48 52 3 -21 -64 -80 -100
-72 -112 -75 -117 -104 -112 -158 -121
-148 -160 -192 -160 -214 -221 -248 -247
-212 -224 -212 -216 -186 -155 -181 -192
-284 -244 -288 -372 -288 -241 -224 -276
-256 -251 -284 -307 -320 -316 -285 -316
-276 -288 -312 -288 -315 -288 -346 -320
-371 -320 -287 -268 -247 -256 -217 -268
-261 -256 -304 -268 -304 -316 -256 -253
-224 -239 -240 -174 -208 -217 -214 -192
-196 -224 -204 -256 -223 -217 -177 -162
-183 -201 -214 -192 -256 -219 -179 -180
-156 -115 -140 -160 -135 -120 -91 -64
-96 -57 -90 -124 -160 -117 -92 -86
-58 -60 -92 -128 -96 -92 -83 -116
-96 -51 0 -52 42 -28 -128 -96
-122 -96 -128 -96 -57 -64 -57 -92
-120 -128 -120 -118 -115 -127 -128 -118
-166 -126 -176 -128 -120 -145 -168 -156
-196 -160 -160 -168 -158 -135 -160 -176
-236 -280 -256 -248 -293 -272 -256 -252
-219 -282 -279 -234 -233 -206 -252 -246
-224 -280 -269 -283 -264 -266 -256 -226
-200 -153 -164 -180 -249 -224 -187 -224
-177 -160 -179 -192 -189 -160 -221 -184
-213 -244 -180 -149 -128 -128 -223 -249
-318 -287 -285 -244 -213 -192 -192 -181
-221 -212 -223 -245 -256 -256 -252 -286
-248 -224 -159 -223 -184 -143 -80 -168
-144 -192 -208 -192 -192 -144 -87 -63
-80 -80 -84 -64 -83 -72 -56 -30
12 0 36 -2 -32 -36 -40 -13
14 20 92 128 128 128 109 83
40 8 68 80 174 186 201 126
135 67 32 42 78 100 134 136
140 138 142 102 96 96 108 68
132 96 98 128 142 105 102 136
104 103 160 136 141 137 136 163
143 136 129 132 160 137 96 68
98 131 139 179 172 154 156 132
84 124 112 124 155 128 103 128
86 135 120 96 27 66 122 79
124 128 137 -9 0 -24 0 -6
17 9 -6 52 48 56 52 32
-70 -80 -171 -104 -102 -120 -88 -59
-93 -64 -91 -63 -88 -147 -180 -160
-156 -115 -86 -30 -23 -56 -64 -128
-88 -117 -115 -53 -64 4 -28 -32
-56 -61 -27 -30 -56 -64 -60 -96
-62 2 5 32 32 13 32 -84
-16 -9 -78 37 45 60 18 39
19 1 11 77 68 56 50 53
33 92 56 83 112 114 68 72
71 38 62 108 113 115 60 51
35 0 24 30 83 72 148 119
147 112 64 46 44 8 36 64
75 96 102 102 128 75 139 98
101 102 72 44 66 96 77 108
108 160 136 101 79 38 40 15
99 96 128 111 128 72 6 33
0 0 8 2 4 -7 42 24
31 39 50 76 67 48 17 65
35 0 52 -6 -53 5 14 16
32 4 24 66 60 81 109 53
17 -4 -8 -12 -60 -7 -8 -1
20 14 16 -29 -7 -32 -29 -38
-31 -64 -64 -96 -118 -50 -96 -86
-92 -123 -64 -83 -64 -122 -121 -128
-117 -116 -127 -121 0 -119 -84 -94
-82 -54 -64 -64 -82 -86 -88 -87
-32 -24 -55 -64 -26 -32 -21 -56
-32 -86 -64 -76 43 -6 22 -14
16 0 0 68 34 32 22 0
5 20 77 64 68 24 7 -32
-51 -30 -30 32 4 0 -8 16
-8 0 -12 -12 -10 22 24 54
108 80 72 8 -7 -86 -128 -96
-52 3 8 4 -24 -32 -58 -64
-64 -53 72 -32 40 -20 -82 -59
-96 -64 -55 -58 -20 14 3 -24
0 -30 38 2 -23 0 -56 -64
-49 32 34 73 66 64 33 -20};
y = rudder` || yawing`;
c = {0.01795 0.02419};
n=nrow(y);
/*-- calibration of data --*/
y = y # (c @ j(n,1,1));
mdel = -1;
lspan = 300; /* local span of data */
maice = 1;
call tsmlomar(arcoef,ev,nar,aic,first,last) data=y maxlag=10
opt = (mdel || lspan || maice) print=1;
proc iml;
y = { 116.8 120.1 123.2 130.2 131.4 125.6 124.5 134.3
135.2 151.8 146.4 139.0 127.8 147.0 165.9 165.5
179.4 190.0 189.8 190.9 203.6 183.5 169.3 144.2
141.5 154.3 169.5 193.0 203.2 192.9 209.4 227.2
263.7 297.8 337.1 361.3 355.2 312.6 309.9 323.7
324.1 355.3 383.4 395.1 412.8 406.0 438.0 446.1
452.5 447.3 475.9 487.7 497.2 529.8 551.0 581.1
617.8 658.1 675.2 706.6 724.7 };
y = y`; /*-- convert to column vector --*/
mdel = 0;
trade = 0;
tvreg = 0;
year = 0;
period= 0;
log = 0;
maxit = 100;
update = .; /* use default update method */
line = .; /* use default line search method */
sigmax = 0; /* no upper bound for variances */
back = 100;
opt = mdel || trade || year || period || log || maxit ||
update || line || sigmax || back;
call tsdecomp(cmp,coef,aic) data=y order=2 sorder=0 nar=2
npred=5 opt=opt icmp={1 3} print=1;
y = y[52:61];
cmp = cmp[52:66,];
print y cmp;
title2 'Seasonal Adjustment';
proc iml;
y =
{ 5447 5412 5215 4697 4344 5426
5173 4857 4658 4470 4268 4116
4675 4845 4512 4174 3799 4847
4550 4208 4165 3763 4056 4058
5008 5140 4755 4301 4144 5380
5260 4885 5202 5044 5685 6106
8180 8309 8359 7820 7623 8569
8209 7696 7522 7244 7231 7195
8174 8033 7525 6890 6304 7655
7577 7322 7026 6833 7095 7022
7848 8109 7556 6568 6151 7453
6941 6757 6437 6221 6346 5880 };
y = y`;
call tsbaysea(trend,season,series,adj,abic)
data=y order=2 sorder=1 npred=12 print=2;
print trend season series adj abic;
title2 'Miscellaneous Time Series Analysis Tools';
proc iml;
c = { 264 235 239 239 275 277 274 334 334 306
308 309 295 271 277 221 223 227 215 223
241 250 270 303 311 307 322 335 335 334
309 262 228 191 188 215 215 249 291 296 };
f = { 690 690 688 690 694 702 702 702 700 702
702 694 708 702 702 708 700 700 702 694
698 694 700 702 700 702 708 708 710 704
704 700 700 694 702 694 710 710 710 708 };
t = { 1152 1288 1288 1288 1368 1456 1656 1496 1744 1464
1560 1376 1336 1336 1296 1296 1280 1264 1280 1272
1344 1328 1352 1480 1472 1600 1512 1456 1368 1280
1224 1112 1112 1048 1176 1064 1168 1280 1336 1248 };
p = { 254.14 253.12 251.85 250.41 249.09 249.19 249.52 250.19
248.74 248.41 249.95 250.64 250.87 250.94 250.96 251.33
251.18 251.05 251.00 250.99 250.79 250.44 250.12 250.19
249.77 250.27 250.74 250.90 252.21 253.68 254.47 254.80
254.92 254.96 254.96 254.96 254.96 254.54 253.21 252.08 };
y = c` || f` || t` || p`;
ar = { .82028 -.97167 .079386 -5.4382,
-.39983 .94448 .027938 -1.7477,
-.42278 -2.3314 1.4682 -70.996,
.031038 -.019231 -.0004904 1.3677,
-.029811 .89262 -.047579 4.7873,
.31476 .0061959 -.012221 1.4921,
.3813 2.7182 -.52993 67.711,
-.020818 .01764 .00037981 -.38154 };
ma = { .083035 -1.0509 .055898 -3.9778,
-.40452 .36876 .026369 -.81146,
.062379 -2.6506 .80784 -76.952,
.03273 -.031555 -.00019776 -.025205 };
coef = ar // ma;
ev = { 188.55 6.8082 42.385 .042942,
6.8082 32.169 37.995 -.062341,
42.385 37.995 5138.8 -.10757,
.042942 -.062341 -.10757 .34313 };
nar = 2; nma = 1;
call tspred(forecast,impulse,mse,y,coef,nar,nma,ev,
5,nrow(y),-1);
observed = y[,{1 2}];
predicted = forecast[,{1 2}];
cname = {y1 y2};
cname1 = {p1 p2};
print observed[colname=cname format= 5.0]
predicted[colname=cname1 format= 8.3];
proc iml;
y = { 2.430 2.506 2.767 2.940 3.169 3.450 3.594 3.774 3.695 3.411
2.718 1.991 2.265 2.446 2.612 3.359 3.429 3.533 3.261 2.612
2.179 1.653 1.832 2.328 2.737 3.014 3.328 3.404 2.981 2.557
2.576 2.352 2.556 2.864 3.214 3.435 3.458 3.326 2.835 2.476
2.373 2.389 2.742 3.210 3.520 3.828 3.628 2.837 2.406 2.675
2.554 2.894 3.202 3.224 3.352 3.154 2.878 2.476 2.303 2.360
2.671 2.867 3.310 3.449 3.646 3.400 2.590 1.863 1.581 1.690
1.771 2.274 2.576 3.111 3.605 3.543 2.769 2.021 2.185 2.588
2.880 3.115 3.540 3.845 3.800 3.579 3.264 2.538 2.582 2.907
3.142 3.433 3.580 3.490 3.475 3.579 2.829 1.909 1.903 2.033
2.360 2.601 3.054 3.386 3.553 3.468 3.187 2.723 2.686 2.821
3.000 3.201 3.424 3.531 };
call tsunimar(ar,v,nar,aic) data=y maxlag=5
opt=({-1 1}) print=1;
/*-- set up complex coefficient matrix --*/
ar_cx = ar || j(nrow(ar),1,0);
call tsroot(root) matin=ar_cx nar=nar
nma=0 print=1;
call tsroot(ar_cx) matin=root nar=nar qcoef=1
nma=0 print=1;
title; title2;