PROC X12: Automatic Outlier Detection :: SAS/ETS(R) 9.2 User's Guide

The X12 Procedure

Example 32.5 Automatic Outlier Detection

This example demonstrates the use of the OUTLIER statement to automatically detect and remove outliers from a time series to be seasonally adjusted. The data set is the same as in the section Basic Seasonal Adjustment and the previous examples. Adding the OUTLIER statement to Example 32.3 requests that outliers be detected by using the default critical value as described in the section OUTLIER Statement. The tables associated with outlier detection for this example are shown in Output 32.5.1. The first table shows the critical values; the second table shows that a single potential outlier was identified; the third table shows the estimates for the ARMA parameters. Since no outliers are included in the regression model, the "Regression Model Parameter Estimates" table is not displayed. Because only a potential outlier was identified, and not an actual outlier, in this case the A1 series and the B1 series are identical.

   title 'Automatic Outlier Identification';
   proc x12 data=sales date=date;
      var sales;
      transform function=log;
      arima model=( (0,1,1)(0,1,1) );
      outlier;
      estimate;
      x11;
      output out=nooutlier a1 b1 d10;
   run ;

Output 32.5.1 PROC X12 Output When Potential Outliers Are Identified

Automatic Outlier Identification

The X12 Procedure

Critical Values to use in Outlier Detection
For variable sales
Begin	SEP1978
End	AUG1990
Observations	144
Method	Add One
AO Critical Value	3.889838
LS Critical Value	3.889838

Note:

The following time series values might later be identified as outliers when data are added or revised. They were not identified as outliers in this run either because their test t-statistics were slightly below the critical value or because they were eliminated during the backward deletion step of the identification procedure, when a non-robust t-statistic is used.

Potential Outliers
For variable sales
Type of Outlier	Date	t Value for AO	t Value for LS
AO	NOV1989	-3.48	-1.51

Exact ARMA Maximum Likelihood Estimation
For variable sales
Parameter	Lag	Estimate	Standard Error	t Value	Pr > \|t\|
Nonseasonal MA	1	0.40181	0.07887	5.09	<.0001
Seasonal MA	12	0.55695	0.07626	7.30	<.0001

In the next example, reducing the critical value to 3.3 causes the outlier identification routine to more aggressively identify outliers as shown in Output 32.5.2. The first table shows the critical values. The second table shows that three additive outliers and a level shift have been included in the regression model. The third table shows how the inclusion of outliers in the model affects the ARMA parameters.

   proc x12 data=sales date=date;
      var sales;
      transform function=log;
      arima model=((0,1,1) (0,1,1));
      outlier cv=3.3;
      estimate;
      x11;
      output out=outlier(obs=50) a1 a8  a8ao a8ls b1 d10;
   run;

   proc print data=outlier(obs=50);
   run;

Output 32.5.2 PROC X12 Output When Outliers Are Identified

Automatic Outlier Identification

The X12 Procedure

Critical Values to use in Outlier Detection
For variable sales
Begin	SEP1978
End	AUG1990
Observations	144
Method	Add One
AO Critical Value	3.3
LS Critical Value	3.3

Regression Model Parameter Estimates
For variable sales
Type	Parameter	NoEst	Estimate	Standard Error	t Value	Pr > \|t\|
Automatically Identified	AO JAN1981	Est	0.09590	0.02168	4.42	<.0001
	LS FEB1983	Est	-0.09673	0.02488	-3.89	0.0002
	AO OCT1983	Est	-0.08032	0.02146	-3.74	0.0003
	AO NOV1989	Est	-0.10323	0.02480	-4.16	<.0001

Exact ARMA Maximum Likelihood Estimation
For variable sales
Parameter	Lag	Estimate	Standard Error	t Value	Pr > \|t\|
Nonseasonal MA	1	0.33205	0.08239	4.03	<.0001
Seasonal MA	12	0.49647	0.07676	6.47	<.0001

The first 50 observations of the A1, A8, A8AO, A8LS, B1, and D10 series are displayed in Output 32.5.3. You can confirm the following relationships from the data.

$\text{[math]}$

The seasonal factors are stored in the variable sales_D10.

Output 32.5.3 PROC X12 Output Series Related to Outlier Detection

Automatic Outlier Identification

Obs	DATE	sales_A1	sales_A8	sales_A8AO	sales_A8LS	sales_B1	sales_D10
1	SEP78	112	1.10156	1.00000	1.10156	101.674	0.90496
2	OCT78	118	1.10156	1.00000	1.10156	107.121	0.94487
3	NOV78	132	1.10156	1.00000	1.10156	119.830	1.04711
4	DEC78	129	1.10156	1.00000	1.10156	117.107	1.00119
5	JAN79	121	1.10156	1.00000	1.10156	109.844	0.94833
6	FEB79	135	1.10156	1.00000	1.10156	122.553	1.06817
7	MAR79	148	1.10156	1.00000	1.10156	134.355	1.18679
8	APR79	148	1.10156	1.00000	1.10156	134.355	1.17607
9	MAY79	136	1.10156	1.00000	1.10156	123.461	1.07565
10	JUN79	119	1.10156	1.00000	1.10156	108.029	0.91844
11	JUL79	104	1.10156	1.00000	1.10156	94.412	0.81206
12	AUG79	118	1.10156	1.00000	1.10156	107.121	0.91602
13	SEP79	115	1.10156	1.00000	1.10156	104.397	0.90865
14	OCT79	126	1.10156	1.00000	1.10156	114.383	0.94131
15	NOV79	141	1.10156	1.00000	1.10156	128.000	1.04496
16	DEC79	135	1.10156	1.00000	1.10156	122.553	0.99766
17	JAN80	125	1.10156	1.00000	1.10156	113.475	0.94942
18	FEB80	149	1.10156	1.00000	1.10156	135.263	1.07172
19	MAR80	170	1.10156	1.00000	1.10156	154.327	1.18663
20	APR80	170	1.10156	1.00000	1.10156	154.327	1.18105
21	MAY80	158	1.10156	1.00000	1.10156	143.433	1.07383
22	JUN80	133	1.10156	1.00000	1.10156	120.738	0.91930
23	JUL80	114	1.10156	1.00000	1.10156	103.490	0.81385
24	AUG80	140	1.10156	1.00000	1.10156	127.093	0.91466
25	SEP80	145	1.10156	1.00000	1.10156	131.632	0.91302
26	OCT80	150	1.10156	1.00000	1.10156	136.171	0.93086
27	NOV80	178	1.10156	1.00000	1.10156	161.589	1.03965
28	DEC80	163	1.10156	1.00000	1.10156	147.972	0.99440
29	JAN81	172	1.21243	1.10065	1.10156	141.864	0.95136
30	FEB81	178	1.10156	1.00000	1.10156	161.589	1.07981
31	MAR81	199	1.10156	1.00000	1.10156	180.653	1.18661
32	APR81	199	1.10156	1.00000	1.10156	180.653	1.19097
33	MAY81	184	1.10156	1.00000	1.10156	167.036	1.06905
34	JUN81	162	1.10156	1.00000	1.10156	147.064	0.92446
35	JUL81	146	1.10156	1.00000	1.10156	132.539	0.81517
36	AUG81	166	1.10156	1.00000	1.10156	150.695	0.91148
37	SEP81	171	1.10156	1.00000	1.10156	155.234	0.91352
38	OCT81	180	1.10156	1.00000	1.10156	163.405	0.91632
39	NOV81	193	1.10156	1.00000	1.10156	175.206	1.03194
40	DEC81	181	1.10156	1.00000	1.10156	164.312	0.98879
41	JAN82	183	1.10156	1.00000	1.10156	166.128	0.95699
42	FEB82	218	1.10156	1.00000	1.10156	197.901	1.09125
43	MAR82	230	1.10156	1.00000	1.10156	208.795	1.19059
44	APR82	242	1.10156	1.00000	1.10156	219.688	1.20448
45	MAY82	209	1.10156	1.00000	1.10156	189.731	1.06355
46	JUN82	191	1.10156	1.00000	1.10156	173.391	0.92897
47	JUL82	172	1.10156	1.00000	1.10156	156.142	0.81476
48	AUG82	194	1.10156	1.00000	1.10156	176.114	0.90667
49	SEP82	196	1.10156	1.00000	1.10156	177.930	0.91200
50	OCT82	196	1.10156	1.00000	1.10156	177.930	0.89970

From the two previous examples, you can examine how outlier detection affects the seasonally adjusted series. Output 32.5.4 shows a plot of A1 versus B1 in the series where outliers are detected. B1 has been adjusted for the additive outliers and the level shift.

   proc sgplot data=outlier;
      series x=date y=sales_A1 / name='A1' markers
                                 markerattrs=(color=red symbol='circle')
                                 lineattrs=(color=red);
      series x=date y=sales_B1 / name='B1' markers
                                 markerattrs=(color=black symbol='asterisk')
                                 lineattrs=(color=black);
      yaxis label='Original and Outlier Adjusted Time Series';
   run;

Output 32.5.4 Original Series and Outlier Adjusted Series

Output 32.5.5 compares the seasonal factors (table D10) of the series unadjusted for outliers to the series adjusted for outliers. The seasonal factors are based on the B1 series.

   data both;
      merge nooutlier(rename=(sales_D10=unadj_D10)) outlier;
   run;
   
   title 'Results of Outlier Identification on Final Seasonal Factors';
   proc sgplot data=both;
      series x=date y=unadj_D10 / name='unadjusted' markers
                                  markerattrs=(color=red symbol='circle')
                                  lineattrs=(color=red)
                                  legendlabel='Unadjusted for Outliers';
      series x=date y=sales_D10 / name='adjusted' markers
                                  markerattrs=(color=blue symbol='asterisk')
                                  lineattrs=(color=blue)
                                  legendlabel='Adjusted for Outliers';
      yaxis label='Final Seasonal Factors';
   run;

Output 32.5.5 Seasonal Factors Based on Original and Outlier Adjusted Series

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