The X12 Procedure

X11 Statement

X11 options ;

The X11 statement is an optional statement for invoking seasonal adjustment by an enhanced version of the methodology of the U.S. Census Bureau X-11 and X-11Q programs. You can control the type of seasonal adjustment decomposition calculated with the MODE= option. The output includes the final tables and diagnostics for the X-11 seasonal adjustment method listed in Table 37.7. Tables E1, E2, E3, C20, D1, and D7 are not displayed by default; however, you can display these tables by requesting them in the TABLES statement.

Table 37.7: Tables Related to X11 Seasonal Adjustment

Table Name	Description
B1	Original series, adjusted for prior effects and forecast extended
C17	Final weights for the irregular component
C20	Final extreme value adjustment factors
D1	Modified original data, D iteration
D7	Preliminary trend cycle, D iteration
D8	Final unmodified SI ratios (differences)
D8A	F tests for stable and moving seasonality, D8
D9	Final replacement values for extreme SI ratios (differences), D iteration
D9A	Moving seasonality ratios for each period
SeasonalFilter	Seasonal filter statistics for Table D10
D10	Final seasonal factors
D10B	Seasonal factors, adjusted for user-defined seasonal
D10D	Final seasonal difference
D11	Final seasonally adjusted series
D11A	Final seasonally adjusted series with forced yearly totals
D11R	Rounded final seasonally adjusted series (with forced yearly totals)
TrendFilter	Trend filter statistics for Table D12
D12	Final trend cycle
D13	Final irregular component
D16	Combined seasonal and trading day factors
D16B	Final adjustment differences
D18	Combined calendar adjustment factors
E1	Original data modified for extremes
E2	Modified seasonally adjusted series
E3	Modified irregular series
E4	Ratio of yearly totals of original and seasonally adjusted series
E5	Percent changes (differences) in original series
E6	Percent changes (differences) in seasonally adjusted series
E6A	Percent changes (differences) in seasonally adjusted series with forced yearly totals (D11.A)
E6R	Percent changes (differences) in rounded seasonally adjusted series (D11.R)
E7	Percent changes (differences) in final trend component series
E8	Percent changes (differences) in original series adjusted for calendar factors (A18)
F2A–F2I	X11 diagnostic summary
F3	Monitoring and quality assessment statistics
F4	Day of the week trading day component factors
G	Spectral plots

For more details about the X-11 seasonal adjustment diagnostics, see Shiskin, Young, and Musgrave (1967), Lothian and Morry (1978a), and Ladiray and Quenneville (2001).

The following options can appear in the X11 statement:

FINAL=AO | LS | TC | USER |ALL FINAL=(options)

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.

FORCE=TOTALS | ROUND | BOTH

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 details, 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.

MODE=ADD | MULT | LOGADD | PSEUDOADD

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 37.8 shows the values of the MODE= option and the corresponding models for the original (O) and the seasonally adjusted (SA) series.

Table 37.8: Modes of Seasonal Adjustment and Their Models

Value of Mode Option	Name	Model for $O$	Model for $SA$
MULT	Multiplicative	$O = C \times S \times I$	$SA = C \times I$
ADD	Additive	$O = C + S + I$	$SA = C + I$
PSEUDOADD	Pseudo-additive	$O = C \times [ S + I - 1 ]$	$SA = C \times I$
LOGADD	Log-additive	$Log(O) = C + S + I$	$SA = exp(C + I)$

OUTFORECAST OUTFCST

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, and D18. 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.

SEASONALMA=S3X1 | S3X3 | S3X5 | S3X9 | S3X15 | STABLE | X11DEFAULT | MSR

specifies which seasonal moving average (also called seasonal “filter”) is used to estimate the seasonal factors. These seasonal moving averages are $n \times m$ 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 U.S. Census Bureau’s X-11-ARIMA program. The default for PROC X12 is SEASONALMA=MSR, which is the methodology of Statistic Canada’s X-11-ARIMA/88 program.

Table 37.9 describes the seasonal filter options available for the entire series:

Table 37.9: X-12-ARIMA Seasonal Filter Options and Descriptions

Filter Name	Description of Filter
S3X1	A $3 \times 1$ moving average
S3X3	A $3 \times 3$ moving average
S3X5	A $3 \times 5$ moving average
S3X9	A $3 \times 9$ moving average
S3X15	A $3 \times 15$ 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	A $3 \times 3$ moving average is used to calculate the
	initial seasonal factors in each iteration, and a $3 \times 5$ 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)

SIGMALIM=(lower limit, upper limit ) SIGMALIM=(lower limit ) SIGMALIM=( , upper limit )

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

Table 37.10: Weights for Irregular Values

Weight	Sigma Limit
$0$	If $\frac{\| I_ t - \mu \|}{\sigma _{1,I_ t}} \geq$ upper limit
Partial weight	If lower limit $< \frac{\| I_ t - \mu \|}{\sigma _{2,I_ t}} <$ upper limit
$1$	If $\frac{\| I_ t - \mu \|}{\sigma _{2,I_ t}} \leq$ lower limit

In Table 37.10, $\mu$ is the theoretical mean of the irregular component, and $\sigma _{1,I_ t}$ and $\sigma _{2,I_ t}$ 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 $\sigma _{1,I_ t}$ and $\sigma _{2,I_ t}$ vary with respect to $t$ , and they are the same if no extreme values are removed. If they are different ( $\sigma _{2,I_ t}$ < $\sigma _{1,I_ t}$ ), then the first line in Table 37.10 is reevaluated with $\sigma _{2,I_ t}$ . In the special case where the lower limit equals the upper limit, the weight is $1$ for $\frac{| I_ t - \mu |}{\sigma _{2,I_ t}} \leq$ 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.

TRENDMA=value

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.

TYPE=SA | SUMMARY | TREND

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).