The X13 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 US 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 45.7. Tables B7, B13, B17, B20, C1, 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 45.7: Tables Related to X11 Seasonal Adjustment

Table Name

Description

B1

Original series, adjusted for prior effects and forecast extended

B7

Preliminary trend-cycle, B iteration

B13

Irregular component, B iteration

B17

Preliminary weights for the irregular component

B20

Extreme values, B iteration

C1

Original series modified for outliers, trading day, and prior factors, C iteration

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

D8B

Final unmodified SI ratios, with labels for outliers and extreme values

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)

E18

Final adjustment ratios (original series to seasonally adjusted series)

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

You can specify the following options 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 45.8 shows the values of the MODE= option and the corresponding models for the original (O) and the seasonally adjusted (SA) series.

Table 45.8: Modes of Seasonal Adjustment and Their Models

Value of Mode Option

Name

Model for O

Model for SA

MULT

Multiplicative

$O = C \times S \times I$

$\mbox{SA} = C \times I$

ADD

Additive

$O = C + S + I$

$\mbox{SA} = C + I$

PSEUDOADD

Pseudo-additive

$O = C \times [ S + I - 1 ]$

$\mbox{SA} = C \times I$

LOGADD

Log-additive

$\log (O) = C + S + I$

$\mbox{SA} = \exp (C + I)$


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, 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.

SEASONALMA=S3X1 | S3X3 | S3X5 | S3X9 | S3X15 | STABLE | X11DEFAULT | MSR
SEASONALMA=(filter-list-by-period)

specifies which seasonal moving average (also called "seasonal filter") to use 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 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 $3 \times 1$ moving average filter to the first quarter of a quarterly series and a $3 \times 3$ moving average to the second, third, and fourth quarters: 

   X11 SEASONALMA=( S3X1 S3X3 S3X3 S3X3 );

Table 45.9 describes the seasonal filter options available for the entire series:

Table 45.9: X-13ARIMA-SEATS 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

Uses a $3 \times 3$ moving average 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)


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

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

Table 45.10: 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 45.10, $\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 45.10 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).