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;

   ... more lines ...

/*--- X-11 ARIMA ---*/
proc x11 data=sales;
   monthly date=date;
   var sales;
   tables d11;
run;

Figure 36.1 Basic Seasonal Adjustment

The X11 Procedure

Seasonal Adjustment of - sales

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.

Selected Tables or 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

Figure 36.2 Basic Seasonal Adjustment

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

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;

proc sgplot data=out;
   series x=date y=sales    / markers
                            markerattrs=(color=red symbol='asterisk')
                            lineattrs=(color=red)
                            legendlabel="original" ;
   series x=date y=adjusted / markers
                            markerattrs=(color=blue symbol='circle')
                            lineattrs=(color=blue)
                            legendlabel="adjusted" ;
   yaxis label='Original and Seasonally Adjusted Time Series';
run;

Figure 36.3 Plot of Original and Seasonally Adjusted Data