X11 – מילון אנגלי-אנגלי
X Window System
X11 output A 1 - Original Series
This
X-11 table will show the original series, prior to any initial user-defined or trading-day adjustment. Note that for quarterly series, no prior adjustment factors can be specified, and the original series will be shown as table
B 1 .
For more information, see
X-11 Census Method II Seasonal Adjustment .
X11 output A 2 - Prior Monthly Adjustment Factors
For
X-11 monthly series, the user may specify a second series that contains prior monthly adjustment factors, for example, in order to adjust for an unusual holiday etc. The factors specified here will be subtracted from the original series for additive models, or will be used to divide the original series if multiplicative seasonal adjustment was requested (thus, the values in this series must be unequal to zero in that case).
For more information, see
X-11 Census Method II Seasonal Adjustment .
X11 output A 3 - Original Series Adjusted by Prior Monthly Adjustment Factors
In this
X-11 monthly series, the factors specified in
A 2 will be subtracted from the original series (additive adjustment) or they will be used to divide the values in the original series (multiplicative adjustment). The resulting adjusted series is shown in this table.
For more information, see
X-11 Census Method II Seasonal Adjustment .
X11 output A 4 - Prior Trading Day Adjustment Factors
This
X-11 table is only available (applicable) when prior trading-day adjustment factors and a multiplicative model were specified. The user may specify a weight for each day (Monday through Friday); those weights are then proportionately adjusted so that they add to 7. The series (
A 1 or
A 3 ) is then divided by monthly calendar factors that are computed based on the number of the respective days in the respective month. Note that by default, the calendar factors are also adjusted for different lengths of different months; however, the length of month variability can also be included in the calendar factors (in which case a constant length of month of 30.4375 is used).
For more information, see
X-11 Census Method II Seasonal Adjustment .
X11 output B 1 - Prior Adjusted Series or Original Series
This
X-11 table shows the original series, or the initial adjusted series, depending on whether or not prior monthly adjustment factors and/or trading day adjustment factors where specified (for quarterly
X-11, B 1 is always the original series).
For more information, see
X-11 Census Method II Seasonal Adjustment .
X11 output B 10 - Seasonal Factors
After replacing extreme values by the corresponding
B 9 values, a 7-term weighted moving average is applied to the S-I differences (ratios) in
B 8 . The resulting estimate of the seasonal factors is then adjusted so that the sum for each year is equal to zero (additive model) or 12.0 (multiplicative model).
For more information, see
X-11 Census Method II Seasonal Adjustment .
X11 output B 11 - Seasonally Adjusted Series
X11 output B 15 - Preliminary Trading-day Regression
X11 output B 16 - Trading-day Adjustment Factors Derived from Regression Coefficients
From the trading-day regression weights, monthly adjustment factors are computed based on the number of particular trading days (i.e., Mondays, Tuesdays, etc.) in the respective months. These factors are printed in this
X-11 table, and are then used to adjust (i.e., subtracted from or divided into) the
B 13 irregular series for trading-day variation.
For more information, see
X-11 Census Method II Seasonal Adjustment .
X11 output B 18 - Trading-day Factors Derived from Combined Daily Weights
This
X-11 table contains the final trading day adjustment factors, computed from the least squares trading-day weights in
B 15 and/or the prior trading-day weights in
A 4 .
For more information, see
X-11 Census Method II Seasonal Adjustment .
X11 output B 19 - Original Series Adjusted for Trading-day and Prior Variation
The values in
B 18 are used to adjust the original (adjusted) series (in
A 1 ,
A 3 , or
B 1 , depending on whether or not prior adjustment factors were specified). Specifically, the values in
B 18 are subtracted from (additive model) or divided into (multiplicative model) the original series.
For more information, see
X-11 Census Method II Seasonal Adjustment .
X11 output B 2 - Trend-cycle
X11 output B 3 - Unmodified S-I Differences or Ratios
X11 output B 4 - Replacement Values for Extreme S-I Differences (Ratios)
First a preliminary estimate of the
X-11 seasonal component is computed by applying a weighted 5-term moving average separately to the
B 3 values for each month. Then a centered 12-term moving average of the preliminary factors for the entire series is computed, and the resulting values are adjusted to sum to zero (additive model) or 12.0 (multiplicative model) within each year. Next an initial estimate of the irregular component is obtained by subtracting from the S-I differences (additive model) or dividing the S-I ratios by the initial estimate for the seasonal component. For the resulting initial estimate of the irregular component, a 5-year sliding standard deviation (s, sigma) is computed, and extreme values in the central year that are beyond 2.5*s are removed. The 5-year sliding s is then recomputed and the process repeated; however, this time a zero weight is assigned to irregular values beyond 2.5*s, a full weight is assigned for values within 1.5*s, and linearly graduated weights between zero and one are assigned for values between 1.5 and 2.5 * s. Values receiving less than full weights are then recomputed as the average of the respective value times its weight and the nearest two full- weight values preceding and following the respective value in that month. Table B 4 shows the final replaced (re-computed) values, and the sliding 5-year s's.
For more information, see
X-11 Census Method II Seasonal Adjustment .
X11 output B 5 - Seasonal Factors
The extreme values in the
B 3 series are replaced by the values shown in
B 4 . From this
X-11 series, preliminary seasonal factors are derived by applying a 5-term moving average to each month separately; then a 12-term moving average is computed for the entire series, and the resulting values adjusted to sum to zero (additive model) or 12.0 (multiplicative model) within each year.
For more information, see
X-11 Census Method II Seasonal Adjustment .
X11 output B 6 - Seasonally Adjusted Series
X11 output B 7 - Trend-cycle
X11 output B 8 - Unmodified S-I Differences (Ratios)
X11 output B 9 - Replacement Values for Extreme S-I Differences (Ratios)
This
X-11 table is the same as
B 4 except that the differences (ratios) in
B 8 are used to which a 7 term moving average is applied (to estimate the seasonal factors).
For more information, see
X-11 Census Method II Seasonal Adjustment .
X11 output C 1 - Original Series Modified by Preliminary Weights and Adjusted for Trading-day and Prior Variation
The series in
B 19 (or
B 1 if no trading-day adjustment was requested) is adjusted for extreme values by the weights computed in
B 17 The resulting modified series in shown in this
X-11 table (C 1).
For more information, see
X-11 Census Method II Seasonal Adjustment .
X11 output C 10 - Seasonal Factors
X11 output C 11 - Seasonally Adjusted Series
X11 output C 13 - Irregular Series
X11 output C 14 - Extreme Irregular Values Excluded from Trading-day Regression
This table is analogous to table
B 14 , and it shows the extreme irregular values (usually beyond 2.5 * s) after re-applying the trading-day routine (based on the monthly trading-day factors shown in
B 16 ).
For more information, see
X-11 Census Method II Seasonal Adjustment .
X11 output C 16 - Final Trading-day Adjustment Factors Derived from Regression X11 output: Coefficients
X11 output C 17 - Final Weights for Irregular Component
X11 output C 18 - Final Trading-day Factors Derived From Combined Daily Weights
X11 output C 19 - Original Series Adjusted for Trading-day and Prior Variation
The values in
C 18 are used to adjust the original (adjusted) series (in
A 3 or
B 1 ). Specifically, the values in
C 18 are subtracted from (additive model) or divided into (multiplicative model) the original series.
For more information, see
X-11 Census Method II Seasonal Adjustment .
X11 output C 2 - Trend-cycle
X11 output C 4 - Modified S-I Differences (Ratios)
To obtain the refined S-I differences (ratios), the values in
C 2 are subtracted from (additive model) or divided into (multiplicative model) the modified series in
C 1 .
For more information, see
X-11 Census Method II Seasonal Adjustment .
X11 output C 5 - Seasonal Factors
X11 output C 6 - Seasonally Adjusted Series
X11 output C 7 - Trend-cycle
The seasonally adjusted series (
C 6 ) is smoothed via a variable moving average procedure (the same procedure used for
B 7 , see also Shiskin, Young, & Musgrave, 1967, for details) to derive the preliminary estimate of the trend-cycle component.
For more information, see
X-11 Census Method II Seasonal Adjustment .
X11 output C 9 - Modified S-I Differences (Ratios)
X11 output D 1 - Original Series Modified by Final Weights and Adjusted for Trading-day and Prior Variation
X11 output D 10 - Final Seasonal Factors
X11 output D 11 - Final Seasonally Adjusted Series
X11 output D 12 - Final Trend-cycle
X11 output D 13 - Final Irregular
X11 output D 2 - Trend-cycle
X11 output D 4 - Modified S-I Differences (Ratios)
X11 output D 5 - Seasonal Factors
X11 output D 6 - Seasonally Adjusted Series
X11 output D 8 - Final Unmodified S-I Differences (Ratios)
The values in the
D 7 series are subtracted from (additive model) or divided into (multiplicative case) the values in
C 19 (or
B 1 if no adjustment for trading-day variation is applied). Then an analysis of variance by month (or quarter) is performed on this series, in order to test for the presence of stable significant seasonality.
For more information, see
X-11 Census Method II Seasonal Adjustment .
X11 output D 9 - Final Replacement Values for Extreme S-I Differences (Ratios)
The values in
D 7 are subtracted from (additive model) or divided into (multiplicative model)
D 1 ; values that are not identical to the corresponding entries in
D 8 are then reported. Also, for each month, the year-to-year difference (additive model) or percent change (multiplicative mode) in the estimates of the irregular and the seasonal components and their ratio (called MSR, moving seasonality ratio) are computed. The MSR may be useful in order to determine the amount of moving seasonality present in each month.
For more information, see
X-11 Census Method II Seasonal Adjustment .
X11 output E 1 Modified Original Series
The values in this
X-11 table are computed by replacing in the original series extreme values (identified by a zero weight in
C 17 ) by the values predicted from the final trend-cycle, seasonal, trading-day (if applicable), and prior adjustment (if applicable) components.
For more information, see
X-11 Census Method II Seasonal Adjustment .
X11 output E 2 - Modified Seasonally Adjusted Series
X11 output E 3 - Modified Irregular Series
The values in this X-11 table are computed by replacing the values in
D 13 with zero (additive model) or 1.0 (multiplicative model) if they were identified as extremes (i.e., assigned zero weight) in
C 17 .
For more information, see
X-11 Census Method II Seasonal Adjustment .
X11 output E 4 - Differences (Ratios) of Annual Totals
These values are computed as the differences (additive model) or ratios (multiplicative model) of the annual totals of (a) the original series
B 1 and the final seasonally adjusted series
D 11 , (b) the modified original series
E 1 and the modified seasonally adjusted series
E 2 .
For more information, see
X-11 Census Method II Seasonal Adjustment .
X11 output E 5 - Differences (Percent Changes) in Original Series
The values in this
X-11 table are computed as the month-to-month (quarter-to-quarter) differences (additive model) or percent changes (multiplicative model) in
B 1 .
For more information, see
X-11 Census Method II Seasonal Adjustment .
X11 output E 6 - Differences (Percent Changes) in Final Seasonally Adjusted Series
X11 output F 2 - Summary Measures
The values in this series are computed by applying an unweighted moving average to the final seasonally adjusted series (
D 11 ). The width of the smoothing window is determined by the month (quarter) for cyclical dominance, or MCD (QCD) for short. The MCD (QCD) is computed as the average span at which the changes in the random component are equal to the changes in the trend-cycle component
For more information, see
X-11 Census Method II Seasonal Adjustment .
X11 output G 1 - Chart
X11 output G 2 - Chart
This line graph will show the final S-I differences (additive model) or ratios (multiplicative model) with the extremes, the final S-I differences (ratios)
without extremes, and the final seasonal factors (i.e.,
D 8 ,
D 9 , and
D 10 , respectively), categorized by month (X-11 monthly) or quarter (X-11 quarterly).
For more information, see
X-11 Census Method II Seasonal Adjustment .
X11 output G 3 - Chart
X11 output G 4 - Chart
X11
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