Building Monthly GDP

/*--------------------------------------------------------------
                    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
  0                 .         13.7156
  0          19.34471         13.7962
  1                 .         13.6888
  0                 .         13.7425
  0          19.32281         13.7425
  1                 .         13.6619
  0                 .         13.7425
  0          19.30315         13.8498
  1                 .          13.984
  0                 .         14.1719
  0          19.60705         14.2256
  1                 .         14.3061
  0                 .          14.333
  0          19.89535         14.1719
  1                 .         14.1988
  0                 .         14.4403
  0          20.21851         14.6282
  1                 .         14.6282
  0                 .         14.5745
  0          20.33155         14.4672
  1                 .         14.5745
  0                 .         14.3867
  0          20.35329         14.2524
  1                 .         14.1182
  0                 .          13.984
  0          20.07522         13.7156
  1                 .         13.6351
  0                 .         13.4472
  0          20.00788         13.4204
  1                 .         13.3935
  0                 .         13.5277
  0          20.22798          13.662
  1                 .          13.152
  0                 .         13.5009
  0          20.04653         13.7425
  1                 .          13.984
  0                 .         14.0377
  0          20.84559          14.494
  1                 .         14.9771
  0                 .         15.3261
  0          21.47592         15.7824
  1                 .         16.2923
  0                 .         16.8023
  0          22.30362          16.695
  1                 .         16.8023
  0                 .         16.7755
  0          22.73435         17.0707
  1                 .         17.1244
  0                 .         17.2318
  0          23.04542         17.3123
  1                 .         17.3391
  0                 .         17.2855
  0          23.44517         17.2049
  1                 .         16.9365
  0                 .         16.7755
  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
  0                 .         17.7686
  0          24.46081         18.4128
  1                 .         18.6007
  0                 .         18.9764
  0          25.26359         19.0838
  1                 .         19.1375
  0                 .         19.2448
  0          25.73372         19.4059
  1                 .         19.4864
  0                 .         19.5938
  0          25.93456         19.5132
  1                 .         19.7548
  0                 .         19.6474
  0          25.78922         19.2448
  1                 .         19.0838
  0                 .         18.6275
  0          25.39786         18.1712
  1                 .          18.037
  0                 .         18.0907
  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
  0                 .         18.5738
  0          26.09272         18.8154
  1                 .         19.2448
  0                 .         19.4864
  0          26.83766         19.9427
  1                 .         20.1843
  0                 .         20.5063
  0          27.27452         20.5332
  1                 .         20.6942
  0                 .         20.6674
  0          27.64128         20.8016
  1                 .         21.1505
  0                 .         21.2042
  0          27.80762         21.2847
  1                 .         21.4189
  0                 .         21.2311
  0          27.70032         21.2311
  1                 .         21.3921
  0                 .         21.2042
  0          27.92872         21.0163
  1                 .         20.3721
  0                 .         21.2042
  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
  0                 .         34.1683
  0          42.19097         34.3293
  1                 .         34.5172
  0                 .         34.5441
  0          42.49152         34.8662
  1                 .         35.1077
  0                 .         34.8661
  0          42.85582         34.9467
  1                 .         35.1115
  0                 .         34.7133
  0          43.24926         34.5176
  1                 .         34.8432
  0                 .         34.5392
  0           43.2872         34.5349
  1                 .         34.4562
  0                 .         35.1164
  0          43.66088         35.0594
  1                 .         35.3449
  0                 .         35.8504
  0          44.01233         36.2365
  1                 .         36.1975
  0                 .         36.3272
  0          44.90609         36.4406
  1                 .         36.4934
  0                 .         36.9027
  0          45.66442         37.0383
  1                 .         36.9815
  0                 .         37.0847
  0          45.99332         37.2251
  1                 .          37.299
  0                 .         37.7815
  0          46.19803         37.9008
  1                 .         38.1301
  0                 .         38.3741
  0          46.91637          38.675
  1                 .         38.5327
  0                 .         38.3871
  0          47.06684         38.7621
  0                 .         38.9667
  1                 .         39.0563
  0                 .         39.0475
  0          47.36143         39.0589
  1                 .         38.6908
  0                 .         38.5869
  0          47.15469         37.8724
  1                 .         37.8474
  0                 .         37.7983
  0          47.07112         37.7011
  1                 .         37.6572
  0                 .         37.5354
  0          47.15441         37.6275
  1                 .         37.5604
  0                 .         37.3015
  0          47.57213         36.5553
  1                 .         36.3339
  0                 .         37.1684
  0          47.08281         37.4543
  1                 .         37.3829
  0                 .         37.3424
  0          48.34349         37.5521
  1                 .         37.7426
  0                 .         37.9009
  0          48.61938         37.7909
  1                 .         37.5716
  0                 .         38.1822
  0           48.9995          38.468
  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
  0                 .          45.344
  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
  0                 .         41.4732
  0          54.21357         41.6418
  1                 .         41.7507
  0                 .         42.2684
  0          54.94446          42.885
  1                 .         43.2957
  0                 .         43.3395
  0           56.1852         43.5878
  1                 .         43.7862
  0                 .         43.7843
  0          56.60972         44.0423
  1                 .         44.3471
  0                 .         44.4774
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  1                 .         45.1442
  0                 .         45.6135
  0          57.32462         45.3646
  1                 .          46.055
  0                 .         46.6286
  0           57.9916         47.0508
  1                 .         47.4509
  0                 .         47.8008
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  1                 .         47.8922
  0                 .         48.1184
  0          60.17586         48.2307
  1                 .         48.2623
  0                 .         48.3303
  0          60.18218          47.672
  1                 .         47.9164
  0                 .         48.8192
  0          60.39158         49.8393
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  1                 .         50.5218
  0                 .         50.6636
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  1                 .          51.445
  0                 .         51.7376
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  1                 .         51.6837
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  1                 .         51.6919
  0                 .          51.685
  0          64.40832         51.6005
  1                 .         51.2595
  0                 .         51.3229
  0           64.8708          51.595
  1                 .         51.5496
  0                 .          51.599
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  1                 .         51.8523
  0                 .         51.6869
  0          65.24912         50.6413
  1                 .         49.4133
  0                 .         48.8003
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  1                 .         48.6125
  0                 .         49.4073
  0          63.82892         50.0203
  1                 .         50.8923
  0                 .         51.1886
  0          65.01184         50.9085
  1                 .         50.6585
  0                 .         50.9285
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  1                 .         51.0228
  0                 .         51.2552
  0          65.87269         51.5854
  1                 .         51.5768
  0                 .         51.2536
  0          66.62858         50.8998
  1                 .         50.3323
  0                 .         49.7768
  0          65.85127         48.8027
  1                 .         49.7531
  0                 .          49.384
  0          64.74973         48.9496
  1                 .         48.6488
  0                 .         48.4896
  0          65.10247         48.3322
  1                 .         47.9335
  0                 .         47.7816
  0            64.868         47.3564
  1                 .         47.1725
  0                 .         46.8316
  0          64.93128         47.7196
  1                 .          47.431
  0                 .          47.814
  0          65.78175         48.3951
  1                 .         48.7317
  0                 .         49.0093
  0          67.28287         49.7543
  1                 .         50.3086
  0                 .         51.0787
  0          68.60022         51.4926
  1                 .         51.6677
  0                 .         51.9253
  0          70.01489         52.9632
  1                 .         53.2164
  0                 .         53.4651
  0          71.40597         53.8086
  1                 .         54.0599
  0                 .         54.2482
  0           72.6601         54.4279
  1                 .         54.4617
  0                 .         54.3773
  0          73.37493          54.306
  1                 .         54.5139
  0                 .         54.5713
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  1                 .         54.6664
  0                 .         54.7455
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  1                 .         54.6782
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  1                 .         54.5707
  0                 .         54.8135
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  1                 .         55.2091
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  1                 .         61.3905
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  1                 .         61.6122
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  1                 .         61.5631
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  1                 .         61.5621
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  1                 .         61.5146
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  1                 .         62.0678
  0                 .         62.3988
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  1                 .         62.4364
  0                 .         62.6392
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  1                 .         62.7314
  0                 .         62.8608
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  1                 .          61.637
  0                 .         61.2198
  0          89.07363         60.9412
  1                 .         60.5393
  0                 .         60.2144
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  1                 .         60.9449
  0                 .         61.5109
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  1                 .         61.5997
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  1                 .         61.9329
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  1                 .         62.3018
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  1                 .         63.3374
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  1                 .         64.1359
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  1                 .         69.1966
  0                 .         69.7795
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  1                 .         71.1135
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  1                 .         71.5868
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  1                 .         72.5149
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  1                 .         72.8672
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  1                 .         73.4143
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  1                 .         75.2056
  0                 .         75.0578
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  1                 .         76.0082
  0                 .         75.9507
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  1                 .         77.0862
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  1                 .         78.6905
  0                 .         78.7482
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  1                 .          79.634
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  1                 .         81.8177
  0                 .           82.55
  0         111.24013         83.2814
  1                 .         83.5471
  0                 .         83.9719
  0         112.10329         84.0422
  1                 .         84.1094
  0                 .          84.402
  0         113.21246         84.9233
  1                 .         84.3698
  0                 .         84.0508
  0         114.31046         85.7994
  1                 .         85.5797
  0                 .          86.241
  0         115.80587          86.206
  1                 .         86.5085
  0                 .         86.9117
  0         117.70686         87.3052
  1                 .         87.4728
  0                 .         87.6419
  0         118.64675         88.3165
  1                 .         88.1778
  0                 .          88.737
  0         119.62524         89.0973
  1                 .         88.7815
  0                 .         89.9689
  0         121.13075         90.4104
  1                 .         91.1008
  0                 .         91.1343
  0         123.23336         91.4065
  1                 .         91.7982
  0                 .          92.472
  0         123.59095          92.671
  1                 .         92.7438
  0                 .         92.6345
  0          125.9253         92.3191
  1                 .         92.6699
  0                 .         92.3486
  0         126.07676         92.3421
  1                 .          92.067
  0                 .         91.3956
  0         126.79338         90.8272
  1                 .         90.5589
  0                 .         90.2884
  0         126.43283         89.6315
  1                 .         89.0366
  0                 .          88.562
  0         127.10303         88.3842
  1                 .         88.0735
  0                 .         87.6361
  0         126.70106         87.1612
  1                 .         87.1764
  0                 .         87.7152
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  1                 .         88.4132
  0                 .         88.8118
  0         128.22258         89.1944
  1                 .         90.0487
  0                 .         89.8366
  0         128.93002         89.8543
  1                 .         89.9448
  0                 .          89.663
  0         129.55769         90.1208
  1                 .         89.6894
  0                 .         90.2943
  0         129.64016         90.5477
  1                 .         90.3587
  0                 .         89.6553
  0         130.31169         89.6978
  1                 .         89.7318
  0                 .         90.2652
  0         131.52089         90.0358
  1                 .         90.5492
  0                 .         90.6137
  0         133.72357         91.3041
  1                 .         91.2014
  0                 .         91.4431
  0          135.2871         91.9245
  1                 .         91.4496
  0                 .         91.7958
  0         136.06509         92.4943
  1                 .         91.7493
  0                 .         92.4549
  0         137.06247         92.4832
  1                 .         92.5476
  0                 .         93.4371
  0         138.30828         93.6306
  1                 .         94.2703
  0                 .         94.7136
  0         139.50376         95.3245
  1                 .         95.2402
  0                 .         95.3681
  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
  0                 .          97.687
  0         145.89585         98.0138
  1                 .         97.8423
  0                 .          97.806
  0         146.02633         97.6811
  1                 .         98.6347
  0                 .         98.1696
  0          147.1693         99.2354
  1                 .         99.3706
  0                 .         100.092
  0         147.26022        100.1357
  1                 .        100.1295
  0                 .        100.1757
  0         148.38664        100.3027
  1                 .        100.6868
  0                 .        100.1968
  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;