X13 Procedure

lists the types of prior adjustment factors, obtained from the EVENT, REGRESSION, and OUTLIER statements, that are to be removed from the final seasonally adjusted series. Additive outliers are removed by specifying FINAL=AO. Level change and ramp outliers are removed by specifying FINAL=LS. Temporary change outliers are removed by specifying FINAL=TC. User-defined regressors or events (USERTYPE=USER) are removed by specifying FINAL=USER. All the preceding are removed by specifying FINAL=ALL or by specifying all the options in parentheses, FINAL=(AO LS TC USER). If this option is not specified, the final seasonally adjusted series contains these effects.

specifies that the seasonally adjusted series be modified to: (a) force the yearly totals of the seasonally adjusted series and the original series to be the same (FORCE=TOTALS), (b) adjust the seasonally adjusted values for each calendar year so that the sum of the rounded seasonally adjusted series for any year equals the rounded annual total (FORCE=ROUND), or (c) first force the yearly totals, then round the adjusted series (FORCE=BOTH). When FORCE=TOTALS is specified, the differences between the annual totals is distributed over the seasonally adjusted values in a way that approximately preserves the month-to-month (or quarter-to-quarter) movements of the original series. For more information, see Huot (1975) and Cholette (1979). This forcing procedure is not recommended if the seasonal pattern is changing or if trading day adjustment is performed. Forcing the seasonally adjusted totals to be the same as the original series annual totals can degrade the quality of the seasonal adjustment, especially when the seasonal pattern is undergoing change. It is not natural if trading day adjustment is performed because the aggregate trading day effect over a year is variable and moderately different from zero.

determines the mode of the seasonal adjustment decomposition to be performed. The four option choices correspond to additive, multiplicative, log-additive, and pseudo-additive decomposition, respectively. If this option is omitted, the procedure performs multiplicative adjustments. Table 8 shows the values of the MODE= option and the corresponding models for the original (O) and the seasonally adjusted (SA) series.

Table 8: Modes of Seasonal Adjustment and Their Models

Value of Mode Option	Name	Model for O	Model for SA
MULT	Multiplicative
ADD	Additive
PSEUDOADD	Pseudo-additive
LOGADD	Log-additive

determines whether forecasts are included in certain tables sent to the output data set. If OUTFORECAST is specified, then forecast values are included in the output data set for Tables A6, A7, A8, A9, A10, B1, D10, D10B, D10D, D16, D16B, D18, and E18. The default is not to include forecasts. The OUTFORECAST option can be specified in either the X11 statement or the FORECAST statement with identical results.

specifies which seasonal moving average (also called "seasonal filter") to use to estimate the seasonal factors. These seasonal moving averages are moving averages, meaning that an n-term simple average is taken of a sequence of consecutive m-term simple averages. X11DEFAULT is the method used by the US Census Bureau’s X-11-ARIMA program.

You can specify either a single filter option or a list. A single option indicates that all periods will use the same filter or the same method of identifying the filter. Alternately, you can specify the seasonal filters for each seasonal period by specifying SEASONALMA=(filter-list-by-period), where (filter-list-by-period) lists the moving average filter for each period. For quarterly data, you must specify four filters; for monthly data, you must specify 12 filters. In the filter-list-by-period, you can specify S3X1, S3X3, S3X5, S3X9, or S3X15. For example, the following statement assigns a moving average filter to the first quarter of a quarterly series and a moving average to the second, third, and fourth quarters:

X11 SEASONALMA=( S3X1 S3X3 S3X3 S3X3 );

Table 9 describes the seasonal filter options available for the entire series:

Table 9: X-13ARIMA-SEATS Seasonal Filter Options and Descriptions

Filter Name	Description of Filter
S3X1	A moving average
S3X3	A moving average
S3X5	A moving average
S3X9	A moving average
S3X15	A moving average
STABLE	Stable seasonal filter: a single seasonal factor for each calendar month or quarter is generated by calculating the simple average of all the values for each month or quarter (taken after detrending and outlier adjustment)
X11DEFAULT	Uses a moving average to calculate the initial seasonal factors in each iteration and a moving average to calculate the final seasonal factors
MSR	Filter chosen automatically by using the moving seasonality ratio of X-11-ARIMA/88 (Dagum 1988)

By default, SEASONALMA=MSR, which is the methodology of Statistic Canada’s X-11-ARIMA/88 program.

specifies the lower and upper sigma limits in standard deviation units which are used to identify and down-weight extreme irregular values in the internal seasonal adjustment computations. One or both limits can be specified. The lower limit must be greater than 0 and not greater than the upper limit. If the lower sigma limit is not specified, then it defaults to a value of 1.5. The default upper sigma limit is 2.5. The comma must be used if the upper limit is specified.

Table 10 shows the effect of the SIGMALIM= option on the weights that are applied to the internal irregular values.

Table 10: Weights for Irregular Values

Weight	Sigma Limit
0	If upper limit
Partial weight	If lower limit upper limit
1	If lower limit

In Table 10, is the theoretical mean of the irregular component, and and are the respective estimates of the standard deviation of the irregular component before and after extreme values are removed. The estimates of the standard deviation and vary with respect to t, and they are the same if no extreme values are removed. If they are different ( < ), then the first line in Table 10 is reevaluated with . In the special case where the lower limit equals the upper limit, the weight is 1 for lower limit, and 0 otherwise. For more information about how extreme irregular values are handled in the X11 computations, see Ladiray and Quenneville; 2001, pp. 53–68, 122–125.

specifies which Henderson moving average is used to estimate the final trend cycle. Any odd number greater than one and less than or equal to 101 can be specified (for example, TRENDMA=23). If the TRENDMA= option is not specified, the program selects a trend moving average based on statistical characteristics of the data. For monthly series, a 9-, 13-, or 23-term Henderson moving average is selected. For quarterly series, the program chooses either a 5- or a 7-term Henderson moving average.

specifies the method used to calculate the final seasonally adjusted series (Table D11). The default method is TYPE=SA. This method assumes that the original series has not been seasonally adjusted. For method TYPE=SUMMARY, the trend cycle, irregular, trading day, and holiday factors are calculated, but not removed from the seasonally adjusted series. Thus, for TYPE=SUMMARY, Table D11 is the same as the original series. For TYPE=TREND, trading day, holiday, and prior adjustment factors are removed from the original series to calculate the seasonally adjusted series (Table D11) and also are used in the calculation of the final trend (Table D12).