The X13 Procedure

OUTLIER Statement

OUTLIER options;

The OUTLIER statement specifies that the X13 procedure perform automatic detection of additive point outliers, temporary change outliers, level-shifts, or any combination of the three when using the specified model. After outliers are identified, the appropriate regression variables are incorporated into the model as "Automatically Identified Outliers," and the model is reestimated. This procedure is repeated until no additional outliers are found.

The OUTLIER statement also identifies potential outliers and lists them in the "Potential Outliers" table in the displayed output. Potential outliers are identified by decreasing the critical value by the value that is specified in the ALMOST= option.

In the output, the initial critical values used for outlier detection in a given analysis are displayed in the table "Critical Values to Use in Outlier Detection." Outliers that are detected and incorporated into the model are displayed in the output in the table "Regression Model Parameter Estimates," where the regression variable is listed as "Automatically Identified."

You can specify the following options:

ALMOST=value

specifies the difference between the critical value for an automatically identified outlier and a potential outlier that is "almost" identified. value is subtracted from the critical value that is used to identify outliers to form a critical value that more aggressively identifies potential outliers. Potential outliers are not included in the regARIMA model. However, potential outliers are displayed in the "Potential Outliers" table. value must be greater than 0. By default, ALMOST=0.5.

ALPHA=value

specifies the significance level to use for outlier identification, where critical values are calculated based on value. Any critical value that is specified in the CV= , AOCV= , LSCV= , or TCCV= option overrides the critical values that are calculated based on this option. value must be greater than 0 and less than or equal to 0.1. If you do not specify this option or the CV= option, the X-13ARIMA-SEATS method calculates the default initial critical value by assuming ALPHA=0.05.

AOCV=value

specifies a critical value to use for additive point outliers. If you specify this option, it overrides any default initial critical value for AO outliers. For more information, see the CV= option .

CV=value

specifies a default initial critical value to use for detecting all types of outliers. The absolute value of the t statistic that is associated with an outlier parameter estimate is compared with value to determine the significance of the outlier. If you do not specify this option, then the default initial critical value is computed based on the ALPHA= option, the CVMETHOD= option, and the number of observations for the model span that is used in the analysis. Table 45.2 shows initial critical values for various series lengths, which are based on the default values of the ALPHA= option and CVMETHOD= option. Increasing the critical value decreases the sensitivity of the outlier detection routine and can reduce the number of observations that are treated as outliers. The automatic model identification process might decrease the critical value by a certain percentage if the automatic model identification process fails to identify an acceptable model.

Table 45.2: Default Critical Values for Outlier Identification

Number of Observations	Outlier Critical Value
1	1.96
2	2.24
3	2.44
4	2.62
5	2.74
6	2.84
7	2.92
8	2.99
9	3.04
10	3.09
11	3.13
12	3.16
24	3.42
36	3.55
48	3.63
72	3.73
96	3.80
120	3.85
144	3.89
168	3.92
192	3.95
216	3.97
240	3.99
264	4.01
288	4.03
312	4.04
336	4.05
360	4.07

CVMETHOD=CORRECTED | LJUNG

specifies the method to use to calculate the default initial critical value, based on the ALPHA= value and the number of observations for the model span that is used in the analysis. You can specify the following values:

CORRECTED: uses a method that is a modification of the Ljung method in which critical values are interpolated based on the number of observations in the model span.
LJUNG: uses a method that is based on the asymptotic formula described in Ljung (1993).

By default, CVMETHOD=CORRECTED.

LSCV=value

specifies a critical value to use for level-shift outliers. If you specify this option, it overrides any default initial critical value for LS outliers. For more information, see the CV= option .

LSRUN=value

specifies the maximum number of successive level-shift outliers to combine to form a temporary level-shift. Valid values for this option are 0 to 5, inclusive. If LSRUN=0 or LSRUN=1, no temporary level-shifts are evaluated. The evaluation of the temporary level-shifts is displayed in the "Tests for Cancellation of Level Shifts" table. By default, LSRUN=0.

METHOD=ADDALL | ADDONE

specifies whether to add outliers one at a time for each model estimation iteration or to add all outliers at once for each model estimation iteration. You can specify the following values:

ADDALL: includes all significant outliers as regressors in the model, and then reestimates the model.
ADDONE: adds the most significant outlier as a regressor in the model, and then reestimates the model.

For both methods, all candidate points for outliers are evaluated at each iteration and model estimation iterations continue until no remaining outliers are identified. By default, METHOD=ADDONE.

SPAN=(mmmyy ,mmmyy ) SPAN=(’yyQq’ ,’yyQq’ )

specifies the dates of the first and last observations to define a subset for searching for outliers. A single date in parentheses is interpreted to be the starting date of the subset. To specify only the ending date, use SPAN=(,mmmyy) or SPAN=(,’yyQq’). If the starting or ending date is omitted, then the first or last date, respectively, of the input data set or BY group is assumed. Because the dates are input as strings and the quarterly dates begin with a numeric character, the specification for a quarterly date must be enclosed in quotation marks. A four-digit year can be specified. If a two-digit year is specified, the value specified in the YEARCUTOFF= SAS system option applies.

TCCV=value

specifies a critical value to use for temporary change (TC) outliers. If you specify this option, it overrides any default initial critical value for TC outliers. For more information, see the CV= option .

TCRATE=value

specifies the rate of decay for temporary change outliers. value must be greater than 0 and less than 1. The default value is $(0.7)^\frac {12}{\Mathtext{period}}$ , where period is the number of observations in one year.

TYPE=NONE TYPE=(outlier types)

lists the outlier types to be detected by the automatic outlier identification method. TYPE=NONE turns off outlier detection. The valid outlier types are AO, LS, and TC. The default is TYPE=(AO LS).