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The X11 Procedure

Basic Seasonal Adjustment

Suppose you have monthly retail sales data starting in September, 1978, in a SAS data set named SALES. At this point you do not suspect that any calendar effects are present and there are no prior adjustments that need to be made to the data.

In this simplest case, you need only specify the DATE= variable in the MONTHLY statement, which associates a SAS date value to each observation. To see the results of the seasonal adjustment, you must request table D11, the final seasonally adjusted series, in a TABLES statement.

   data sales;
      input sales @@;
      date = intnx( 'month', '01sep1978'd, _n_-1 );
      format date monyy7.;
      datalines;
   run;
   
   proc x11 data=sales;
      monthly date=date;
      var sales;
      tables d11;
   run;

 
The X11 Procedure

X-11 Seasonal Adjustment Program
U. S. Bureau of the Census
Economic Research and Analysis Division
November 1, 1968
 
The X-11 program is divided into seven major parts.
Part Description
A. Prior adjustments, if any
B. Preliminary estimates of irregular component weights
and regression trading day factors
C. Final estimates of above
D. Final estimates of seasonal, trend-cycle and
irregular components
E. Analytical tables
F. Summary measures
G. Charts
 
Series - sales
Period covered - 9/1978 to 8/1990
Type of run: multiplicative seasonal adjustment.
No printout. No charts.
Sigma limits for graduating extreme values are 1.5 and 2.5
Irregular values outside of 2.5-sigma limits are excluded
from trading day regression

 
The X11 Procedure
Seasonal Adjustment of - sales

D11 Final Seasonally Adjusted Series
Year JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC Total
1978 . . . . . . . . 123.507 125.776 124.735 129.870 503.887
1979 124.935 126.533 125.282 125.650 127.754 129.648 127.880 129.285 126.562 134.905 133.356 136.117 1547.91
1980 128.734 139.542 143.726 143.854 148.723 144.530 140.120 153.475 159.281 162.128 168.848 165.159 1798.12
1981 176.329 166.264 167.433 167.509 173.573 175.541 179.301 182.254 187.448 197.431 184.341 184.304 2141.73
1982 186.747 202.467 192.024 202.761 197.548 206.344 211.690 213.691 214.204 218.060 228.035 240.347 2513.92
1983 233.109 223.345 218.179 226.389 224.249 227.700 222.045 222.127 222.835 212.227 230.187 232.827 2695.22
1984 238.261 239.698 246.958 242.349 244.665 247.005 251.247 253.805 264.924 266.004 265.366 277.025 3037.31
1985 275.766 282.316 294.169 285.034 294.034 296.114 294.196 309.162 311.539 319.518 318.564 323.921 3604.33
1986 325.471 332.228 330.401 330.282 333.792 331.349 337.095 341.127 346.173 350.183 360.792 362.333 4081.23
1987 363.592 373.118 368.670 377.650 380.316 376.297 379.668 375.607 374.257 372.672 368.135 364.150 4474.13
1988 370.966 384.743 386.833 405.209 380.840 389.132 385.479 377.147 397.404 403.156 413.843 416.142 4710.89
1989 428.276 418.236 429.409 446.467 437.639 440.832 450.103 454.176 460.601 462.029 427.499 485.113 5340.38
1990 480.631 474.669 486.137 483.140 481.111 499.169 485.370 485.103 . . . . 3875.33
Avg 277.735 280.263 282.435 286.358 285.354 288.638 288.683 291.413 265.728 268.674 268.642 276.442  

Total: 40324 Mean: 280.03 S.D.: 111.31

Figure 21.1: Basic Seasonal Adjustment

You can compare the original series, table B1, and the final seasonally adjusted series, table D11 by plotting them together. These tables are requested and named in the OUTPUT statement.

   title 'Monthly Retail Sales Data (in $1000)';
   
   proc x11 data=sales noprint;
      monthly date=date;
      var sales;
      output out=out b1=sales d11=adjusted;
   run;
   
   symbol1 i=join v='star';
   symbol2 i=join v='circle';
   legend1 label=none value=('original' 'adjusted');
   
   proc gplot data=out;
      plot sales    * date = 1
           adjusted * date = 2 / overlay legend=legend1;
   run;

x11gs03.gif (6116 bytes)

Figure 21.2: Plot of Original and Seasonally Adjusted Data

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