The SAS System

The X12 Procedure


Note: This release of the X12 procedure is based on the Census Bureau X-13ARIMA-SEATS Release Version 1.1.

Table A 1: Time Series Data (for the Span Analyzed)
For Variable sales
Year JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC Total
1978 . . . . . . . . 112.000 118.000 132.000 129.000 491.000
1979 121.000 135.000 148.000 148.000 136.000 119.000 104.000 118.000 115.000 126.000 141.000 135.000 1546.00
1980 125.000 149.000 170.000 170.000 158.000 133.000 114.000 140.000 145.000 150.000 178.000 163.000 1795.00
1981 172.000 178.000 199.000 199.000 184.000 162.000 146.000 166.000 171.000 180.000 193.000 181.000 2131.00
1982 183.000 218.000 230.000 242.000 209.000 191.000 172.000 194.000 196.000 196.000 236.000 235.000 2502.00
1983 229.000 243.000 264.000 272.000 237.000 211.000 180.000 201.000 204.000 188.000 235.000 227.000 2691.00
1984 234.000 264.000 302.000 293.000 259.000 229.000 203.000 229.000 242.000 233.000 267.000 269.000 3024.00
1985 270.000 315.000 364.000 347.000 312.000 274.000 237.000 278.000 284.000 277.000 317.000 313.000 3588.00
1986 318.000 374.000 413.000 405.000 355.000 306.000 271.000 306.000 315.000 301.000 356.000 348.000 4068.00
1987 355.000 422.000 465.000 467.000 404.000 347.000 305.000 336.000 340.000 318.000 362.000 348.000 4469.00
1988 363.000 435.000 491.000 505.000 404.000 359.000 310.000 337.000 360.000 342.000 406.000 396.000 4708.00
1989 420.000 472.000 548.000 559.000 463.000 407.000 362.000 405.000 417.000 391.000 419.000 461.000 5324.00
1990 472.000 535.000 622.000 606.000 508.000 461.000 390.000 432.000 . . . . 4026.00
Avg 271.833 311.667 351.333 351.083 302.417 266.583 232.833 261.833 241.750 235.000 270.167 267.083  

Total: 40363 Mean: 280.3 S.D.: 119.55
Min: 104 Max: 622



NOTE: Visually significant residual peaks have been found in the spectral plot of the differenced original series starting in SEP1982. The peaks include 4 Seasonal.

Table G 0: 10*LOG(SPECTRUM) of the differenced Original Series (Table A1 or B1)
Spectrum estimated from SEP1982 to AUG1990.
For Variable sales
Type Approximate
Frequency		 Spectrum Estimator
None 0.00 13.3079
None 0.10 14.2357
None 0.20 17.0902
None 0.30 21.1715
None 0.40 21.7900
None 0.50 20.4629
None 0.60 21.0619
None 0.70 23.9332
None 0.80 28.8631
None 0.90 35.1277
Seasonal 1.00 45.4418
None 1.10 34.0398
None 1.20 28.4390
None 1.30 26.5655
None 1.40 26.3683
None 1.50 25.9201
None 1.60 25.0141
None 1.70 25.2504
None 1.80 27.7537
None 1.90 33.8782
Seasonal 2.00 44.9416
None 2.10 35.6738
None 2.20 28.4957
None 2.30 23.5150
None 2.40 20.7161
None 2.50 19.8608
None 2.60 20.7960
None 2.70 23.4016
None 2.80 27.2453
None 2.90 32.1804
Seasonal 3.00 39.8627
None 3.10 28.5591
None 3.20 22.6140
None 3.30 19.8323
None 3.40 18.9495
None 3.50 19.3326
Trading 3.60 20.4196
None 3.70 21.9448
None 3.80 24.5546
None 3.90 30.3512
Seasonal 4.00 39.0213
None 4.10 30.2324
Trading 4.20 25.9678
None 4.30 24.5205
None 4.40 23.1544
None 4.50 21.7462
None 4.60 21.0722
None 4.70 21.7436
None 4.80 24.0627
None 4.90 28.5654
Seasonal 5.00 36.5304
None 5.10 34.5559
Trading 5.20 27.8008
None 5.30 24.1764
None 5.40 22.1754
None 5.50 21.7370
None 5.60 22.0309
None 5.70 22.6542
None 5.80 23.4361
None 5.90 24.2949
Seasonal 6.00 24.7345

Approximate Frequency = 5.20 Percent of Range = 0.45102 Approximate Frequency = 4.20 Percent of Range = 0.39397 Approximate Frequency = 3.60 Percent of Range = 0.22131 Approximate Frequency = 6.00 Percent of Range = 0.35559 Approximate Frequency = 5.00 Percent of Range = 0.72268 Approximate Frequency = 4.00 Percent of Range = 0.80019 Approximate Frequency = 3.00 Percent of Range = 0.82638 Approximate Frequency = 2.00 Percent of Range = 0.98444 Approximate Frequency = 1.00 Percent of Range = 1.00000 Approximate Frequency = 5.90 Percent of Range = 0.34191 Approximate Frequency = 5.80 Percent of Range = 0.31519 Approximate Frequency = 5.70 Percent of Range = 0.29086 Approximate Frequency = 5.60 Percent of Range = 0.27146 Approximate Frequency = 5.50 Percent of Range = 0.26231 Approximate Frequency = 5.40 Percent of Range = 0.27595 Approximate Frequency = 5.30 Percent of Range = 0.33823 Approximate Frequency = 5.10 Percent of Range = 0.66123 Approximate Frequency = 4.90 Percent of Range = 0.47481 Approximate Frequency = 4.80 Percent of Range = 0.33469 Approximate Frequency = 4.70 Percent of Range = 0.26252 Approximate Frequency = 4.60 Percent of Range = 0.24162 Approximate Frequency = 4.50 Percent of Range = 0.26260 Approximate Frequency = 4.40 Percent of Range = 0.30642 Approximate Frequency = 4.30 Percent of Range = 0.34893 Approximate Frequency = 4.10 Percent of Range = 0.52669 Approximate Frequency = 3.90 Percent of Range = 0.53038 Approximate Frequency = 3.80 Percent of Range = 0.34999 Approximate Frequency = 3.70 Percent of Range = 0.26878 Approximate Frequency = 3.50 Percent of Range = 0.18749 Approximate Frequency = 3.40 Percent of Range = 0.17557 Approximate Frequency = 3.30 Percent of Range = 0.20304 Approximate Frequency = 3.20 Percent of Range = 0.28960 Approximate Frequency = 3.10 Percent of Range = 0.47461 Approximate Frequency = 2.90 Percent of Range = 0.58731 Approximate Frequency = 2.80 Percent of Range = 0.43373 Approximate Frequency = 2.70 Percent of Range = 0.31411 Approximate Frequency = 2.60 Percent of Range = 0.23303 Approximate Frequency = 2.50 Percent of Range = 0.20393 Approximate Frequency = 2.40 Percent of Range = 0.23054 Approximate Frequency = 2.30 Percent of Range = 0.31764 Approximate Frequency = 2.20 Percent of Range = 0.47264 Approximate Frequency = 2.10 Percent of Range = 0.69602 Approximate Frequency = 1.90 Percent of Range = 0.64014 Approximate Frequency = 1.80 Percent of Range = 0.44955 Approximate Frequency = 1.70 Percent of Range = 0.37165 Approximate Frequency = 1.60 Percent of Range = 0.36429 Approximate Frequency = 1.50 Percent of Range = 0.39249 Approximate Frequency = 1.40 Percent of Range = 0.40644 Approximate Frequency = 1.30 Percent of Range = 0.41257 Approximate Frequency = 1.20 Percent of Range = 0.47088 Approximate Frequency = 1.10 Percent of Range = 0.64517 Approximate Frequency = 0.90 Percent of Range = 0.67903 Approximate Frequency = 0.80 Percent of Range = 0.48407 Approximate Frequency = 0.70 Percent of Range = 0.33066 Approximate Frequency = 0.60 Percent of Range = 0.24130 Approximate Frequency = 0.50 Percent of Range = 0.22266 Approximate Frequency = 0.40 Percent of Range = 0.26396 Approximate Frequency = 0.30 Percent of Range = 0.24471 Approximate Frequency = 0.20 Percent of Range = 0.11770 Approximate Frequency = 0.10 Percent of Range = 0.02887 Approximate Frequency = 0.00 Percent of Range = 0.00000
Spectral Plot