/*--------------------------------------------------------------
SAS Sample Library
Name: ssmex16.sas
Description: Example program from SAS/ETS User's Guide,
The SSM Procedure
Title: Building Monthly GDP
Product: SAS/ETS Software
Keys: Multivariate Modeling, Temporal Distribution
PROC: SSM
Notes:
--------------------------------------------------------------*/
data useco;
input startQ gdp indpro;
date = intnx('month','01jan1947'd, _n_-1);
format date date.;
datalines;
1 . 13.6351
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0 19.32281 13.7425
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0 19.30315 13.8498
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1 . 14.1988
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0 20.21851 14.6282
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0 20.35329 14.2524
1 . 14.1182
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0 20.07522 13.7156
1 . 13.6351
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1 . 13.3935
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0 20.22798 13.662
1 . 13.152
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0 20.04653 13.7425
1 . 13.984
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1 . 14.9771
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1 . 16.2923
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1 . 16.8023
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0 22.73435 17.0707
1 . 17.1244
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0 23.04542 17.3123
1 . 17.3391
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1 . 16.9365
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0 23.92808 16.8828
1 . 16.856
0 . 16.9902
0 23.98105 17.0976
1 . 17.2854
0 . 17.3928
0 24.23457 17.4465
1 . 17.2854
0 . 17.1244
0 24.28516 16.9634
1 . 16.6949
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0 24.46081 18.4128
1 . 18.6007
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0 25.93456 19.5132
1 . 19.7548
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0 25.78922 19.2448
1 . 19.0838
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0 25.39786 18.1712
1 . 18.037
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0 25.28043 17.9833
1 . 17.8759
0 . 17.9833
0 25.30689 18.037
1 . 18.0638
0 . 18.037
0 25.59397 18.0638
1 . 18.2786
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1 . 19.2448
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1 . 20.1843
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1 . 20.6942
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0 27.64128 20.8016
1 . 21.1505
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1 . 21.4189
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1 . 21.3921
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1 . 20.3721
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0 27.90588 21.6873
1 . 21.8752
0 . 21.6873
0 28.36238 22.0094
1 . 21.9289
0 . 22.1437
0 28.54517 22.1168
1 . 21.8215
0 . 21.741
0 28.48186 21.7947
1 . 21.9289
0 . 21.9289
0 28.75927 21.741
1 . 21.4189
0 . 20.909
0 28.46446 20.5063
1 . 20.1306
0 . 19.7011
0 27.72654 19.4596
1 . 19.1375
0 . 19.3253
0 27.90948 19.8353
1 . 20.1306
0 . 20.5332
0 28.55472 20.7211
1 . 20.9626
0 . 21.58
0 29.22264 21.6068
1 . 21.9289
0 . 22.3584
0 29.76629 22.6805
1 . 23.1636
0 . 23.5125
0 30.49011 23.5394
1 . 22.9757
0 . 22.1973
0 30.43139 22.1705
1 . 22.0094
0 . 22.1436
0 30.55104 23.5125
1 . 24.1298
0 . 23.9151
0 31.23162 23.7004
1 . 23.5125
0 . 23.4857
0 31.1131 23.1904
1 . 23.1099
0 . 23.0831
0 31.19057 22.8415
1 . 22.8147
0 . 22.4926
0 30.813 22.0631
1 . 22.09
0 . 22.0631
0 31.02251 22.1973
1 . 22.6536
0 . 23.0025
0 31.59918 23.3246
1 . 23.593
0 . 23.8078
0 32.12606 23.7809
1 . 24.2372
0 . 24.613
0 32.77717 24.8277
1 . 24.613
0 . 25.0156
0 33.36753 25.1498
1 . 25.2035
0 . 25.1766
0 33.72706 25.123
1 . 25.3645
0 . 25.3914
0 34.04833 25.5524
1 . 25.5793
0 . 25.6866
0 34.18046 25.6866
1 . 25.8745
0 . 26.1698
0 34.5608 26.3308
1 . 26.5724
0 . 26.8945
0 35.01134 26.975
1 . 26.8676
0 . 26.9213
0 35.69479 27.1897
1 . 27.3776
0 . 27.5118
0 35.94954 27.4581
1 . 27.6997
0 . 27.8876
0 36.72708 27.8876
1 . 28.3439
0 . 28.5049
0 37.16382 28.5854
1 . 28.7733
0 . 28.9612
0 37.66862 29.0686
1 . 28.6659
0 . 29.5517
0 37.80219 29.9006
1 . 30.2227
0 . 30.4106
0 38.73452 30.8132
1 . 30.9474
0 . 31.189
0 39.26406 31.4305
1 . 31.7258
0 . 31.86
0 40.06152 31.9405
1 . 32.2626
0 . 32.3968
0 41.00631 32.7994
1 . 33.1215
0 . 33.3363
0 42.01891 33.7925
1 . 33.8462
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0 42.19097 34.3293
1 . 34.5172
0 . 34.5441
0 42.49152 34.8662
1 . 35.1077
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1 . 35.1115
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1 . 34.8432
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0 43.2872 34.5349
1 . 34.4562
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1 . 35.3449
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1 . 37.299
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1 . 38.1301
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1 . 38.5327
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0 47.06684 38.7621
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1 . 39.0563
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1 . 38.6908
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1 . 37.8474
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1 . 37.5604
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1 . 37.3829
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1 . 37.5716
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1 . 38.6313
0 . 39.0772
0 49.14261 40.0157
1 . 40.3955
0 . 40.694
0 50.02436 41.1164
1 . 41.0952
0 . 41.2034
0 51.18278 41.1879
1 . 41.7352
0 . 42.0547
0 51.65448 42.6321
1 . 43.1184
0 . 43.6139
0 52.51226 43.9001
1 . 44.563
0 . 44.5844
0 53.80502 44.5103
1 . 44.7949
0 . 44.8241
0 54.41504 45.016
1 . 44.9347
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0 54.11935 45.6563
1 . 45.8834
0 . 45.7719
0 54.62397 45.4415
1 . 45.3088
0 . 45.3135
0 54.17024 45.186
1 . 45.5153
0 . 45.472
0 54.31265 45.4708
1 . 45.0331
0 . 45.0658
0 53.78679 44.8969
1 . 43.4159
0 . 41.8924
0 53.57166 41.3111
1 . 40.3562
0 . 39.9284
0 52.92444 39.9825
1 . 39.8893
0 . 40.1595
0 53.3322 40.5909
1 . 40.9584
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0 54.21357 41.6418
1 . 41.7507
0 . 42.2684
0 54.94446 42.885
1 . 43.2957
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0 56.1852 43.5878
1 . 43.7862
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0 56.60972 44.0423
1 . 44.3471
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1 . 45.1442
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1 . 46.055
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1 . 50.0106
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1 . 55.6593
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0 81.58035 59.6354
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1 . 60.5286
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0 83.39324 60.9879
1 . 60.918
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0 84.4951 61.1063
1 . 61.3905
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1 . 61.5997
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1 . 64.7218
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1 . 65.1755
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0 95.26337 65.9414
1 . 66.2823
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0 96.53509 66.5732
1 . 67.2551
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0 97.48156 67.9941
1 . 68.4527
0 . 68.5674
0 98.81384 68.9525
1 . 69.1966
0 . 69.7795
0 99.39655 70.2111
1 . 70.9325
0 . 71.0773
0 100.52518 71.0101
1 . 71.1135
0 . 71.0925
0 100.86878 71.3036
1 . 71.5868
0 . 71.2946
0 101.22122 72.246
1 . 72.5149
0 . 72.4092
0 102.08772 72.5899
1 . 72.8672
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1 . 73.4143
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1 . 75.2056
0 . 75.0578
0 105.29379 75.5237
1 . 76.0082
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1 . 77.0862
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1 . 78.6905
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1 . 85.5797
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1 . 86.5085
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1 . 87.4728
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1 . 88.0735
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1 . 90.5492
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1 . 91.2014
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1 . 91.4496
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1 . 91.7493
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1 . 92.5476
0 . 93.4371
0 138.30828 93.6306
1 . 94.2703
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0 139.50376 95.3245
1 . 95.2402
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0 140.99081 95.5331
1 . 95.912
0 . 95.7242
0 141.72695 95.8708
1 . 93.9661
0 . 95.1806
0 142.91757 96.1177
1 . 96.669
0 . 96.7856
0 143.73438 96.8261
1 . 97.0742
0 . 97.44
0 145.46119 97.3002
1 . 97.6752
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1 . 97.8423
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0 146.02633 97.6811
1 . 98.6347
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0 147.1693 99.2354
1 . 99.3706
0 . 100.092
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1 . 100.1295
0 . 100.1757
0 148.38664 100.3027
1 . 100.6868
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0 149.38467 100.7645
1 . 100.7407
0 . 100.4921
0 149.91784 100.2213
1 . 99.9541
0 . 99.2345
0 148.8945 98.7761
1 . 98.579
0 . 98.0964
0 149.63357 96.5934
1 . 92.5289
0 . 93.3148
0 148.91643 92.121
1 . 89.5075
0 . 87.5382
0 145.76985 86.9117
1 . 85.6157
0 . 84.9483
0 143.75018 84.0497
1 . 83.732
0 . 84.567
0 143.55558 85.3735
1 . 85.9988
0 . 86.3075
0 144.02477 86.6403
1 . 86.93
0 . 87.99
0 145.41901 88.2232
1 . 88.8923
0 . 89.2429
0 146.04845 90.6351
1 . 90.8407
0 . 91.4132
0 147.45933 91.673
1 . 91.9146
0 . 91.6296
0 148.45458 91.8108
1 . 92.5893
0 . 92.6124
0 149.39001 92.1015
1 . 93.0194
0 . 92.5816
0 148.81301 92.8754
1 . 93.0939
0 . 93.6897
0 149.89555 94.1465
1 . 94.2426
0 . 94.7279
0 150.21149 94.8324
1 . 95.1997
0 . 96.015
0 151.90255 96.375
1 . 96.0067
0 . 96.7966
0 152.75047 97.1123
1 . 97.1618
0 . 97.7061
0 153.36735 97.1146
1 . 97.3865
0 . 97.3111
0 154.31335 98.2597
1 . 98.3571
0 . 98.4084
0 154.33702 99.0438
1 . 99.488
0 . 99.3112
0 155.38441 99.4162
1 . 99.6083
0 . 99.4432
0 156.06591 99.9987
1 . 100.7177
0 . 100.819
0 157.79938 101.375
1 . 101.5572
0 . 101.3061
0 159.16208 102.2567
1 . 103.1059
0 . 103.1885
0 158.31652 103.6839
1 . 104.105
0 . 104.4671
0 160.10405 104.3507
0 . 105.2863
1 . 105.2619
0 . 106.6291
0 161.50614 106.5114
;
proc print data=useco(obs=8) noobs;
var date startQ gdp indpro;
run;
proc ssm data=useco opt(maxiter=100);
id date interval=month;
/* Bivariate integrated random walk */
state irwState(2) type=ll(slopecov(g));
comp irwInd = irwState[1];
comp irwGdp = irwState[2];
/* Bivariate cycle */
state cycle(2) type=cycle cov(g);
comp cycInd = cycle[1];
comp cycGdp = cycle[2];
/* Bivariate white noise */
state noise(2) type=wn cov(g);
comp noiseInd = noise[1];
comp noiseGdp = noise[2];
/* Observation equations */
model indpro = irwInd cycInd noiseInd;
model gdp = irwGdp cycGdp noiseGdp / distribute(start=startQ);
/* Components for output */
eval trendCycGdp = irwGdp + cycGdp;
eval trendCycInd = irwInd + cycInd;
eval monthlyGdp = irwGdp + cycGdp + noiseGdp;
/* Output data set */
output out=forGdp pdv press;
run;
proc sgplot data=forGdp;
title "Smoothed estimate of the monthly GDP";
series x=date y=smoothed_monthlyGDP;
run;
proc sgplot data=forGdp;
title "Smoothed trend cycle of the monthly GDP";
where year(date) >= 1950 & year(date) < 1960;
series x=date y=smoothed_trendCycGdp;
run;
title;