For more information, see X-11 Census Method II Seasonal Adjustment.

X11 output: A 2. Prior Monthly Adjustment Factors. ForFor more information, see X-11 Census Method II Seasonal Adjustment.

X11 output: A 3. Original Series Adjusted by Prior Monthly Adjustment Factors. In thisFor more information, see X-11 Census Method II Seasonal Adjustment.

X11 output: A 4. Prior Trading Day Adjustment Factors. ThisFor more information, see X-11 Census Method II Seasonal Adjustment.

X11 output: B 1. Prior Adjusted Series or Original Series. ThisFor more information, see X-11 Census Method II Seasonal Adjustment.

X11 output: B 2. Trend-cycle.For more information, see X-11 Census Method II Seasonal Adjustment.

initial trend-cycle estimate is computed as a centered 12-term moving average of B 1. X11 output: B 3. Unmodified S-I Differences or Ratios. An initial estimate of the combined irregular and seasonal component is obtained by subtracting B 2 from B 1 (additive model) or dividing B 1 by B 2 (multiplicative model).For more information, see X-11 Census Method II Seasonal Adjustment.

X11 output: B 4. Replacement Values for Extreme S-I Differences (Ratios). First a preliminary estimate of theFor 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 thisFor more information, see X-11 Census Method II Seasonal Adjustment.

X11 output: B 6. Seasonally Adjusted Series. The preliminary seasonally adjusted series is obtained by subtracting from B 1 (additive model) or dividing B 1 (multiplicative model) by the seasonal factors in B 5.For more information, see X-11 Census Method II Seasonal Adjustment.

X11 output: B 7. Trend-cycle. TheFor more information, see X-11 Census Method II Seasonal Adjustment.

X11 output: B 8. Unmodified S-I Differences (Ratios). ThisFor more information, see X-11 Census Method II Seasonal Adjustment.

X11 output: B 9. Replacement Values for Extreme S-I Differences (Ratios). ThisFor 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. ThisFor more information, see X-11 Census Method II Seasonal Adjustment.

X11 output: B 13. Irregular Series. The trend-cycle estimates in B 7 are subtracted from the seasonally adjusted series in B 11 (additive model), or the B 7 values are used to divide the series in B 11 (multiplicative model). The resulting series is an improved estimate of the irregular series.For more information, see X-11 Census Method II Seasonal Adjustment.

X11 output: B 14. Extreme Irregular Values Excluded from Trading-day Regression. The months in the series are sorted into different groups, depending on the particular day when the month begins (30-day, 31-day months, and Februarys are treated separately). Then extreme values (beyond 2.5 * s; different s values can also be specified) are identified within each type of month in a two-step procedure. The final extreme values that will be excluded are shown in thisFor more information, see X-11 Census Method II Seasonal Adjustment.

X11 output: B 15. Preliminary Trading-day Regression. After removing the B 14 extreme values from B 13, least squares estimates for the seven daily weights are computed.For more information, see X-11 Census Method II Seasonal Adjustment.

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 thisFor more information, see X-11 Census Method II Seasonal Adjustment.

X11 output: B 17. Preliminary Weights for Irregular Component. The estimates of the irregular component (in B 13 or adjusted by B 16, depending on whether or not a trading-day adjustment was performed) are further refined by computing graduated weights for extreme values, depending on their relative (in terms of a sliding 5-year s) distance from 0. Specifically, a process analogous to that described in B 4 above is used. ThisFor more information, see X-11 Census Method II Seasonal Adjustment.

X11 output: B 18. Trading-day Factors Derived from Combined Daily Weights. ThisFor 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: 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 thisFor more information, see X-11 Census Method II Seasonal Adjustment.

X11 output: C 2. Trend-cycle. An estimate of the combined trend-cycle component is computed from C 1 by applying a centered 12-term moving average.For more information, see X-11 Census Method II Seasonal Adjustment.

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. These values are the same as those in B 5, except that the C 4 differences (ratios) are used.For more information, see X-11 Census Method II Seasonal Adjustment.

X11 output: C 6. Seasonally Adjusted Series. The preliminary seasonally adjusted series is computed by subtracting C 5 from (or dividing C 5 into) C 1.For more information, see X-11 Census Method II Seasonal Adjustment.

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). The modified S-I differences (ratios) are computed by subtracting C 7 from (additive models) or dividing C 7 into (multiplicative models) the C 1 series.For more information, see X-11 Census Method II Seasonal Adjustment.

X11 output: C 10. Seasonal Factors. The seasonal factors are computed analogously to B 10, but based on the C 9 S-I differences (ratios).For more information, see X-11 Census Method II Seasonal Adjustment.

X11 output: C 11. Seasonally Adjusted Series. The refined seasonally adjusted series is computed by subtracting from B 1 (additive model) or dividing B 1 by (multiplicative model) the values in C 10.For more information, see X-11 Census Method II Seasonal Adjustment.

X11 output: C 13. Irregular Series. The refined estimate of the irregular (random) component is computed by subtracting from C 11 (additive model) or dividing C 11 by (multiplicative model) the values in C 7.For more information, see X-11 Census Method II Seasonal Adjustment.

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 15. Final Trading-day Regression. ThisFor 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. ThisFor more information, see X-11 Census Method II Seasonal Adjustment.

X11 output: C 17. Final Weights for Irregular Component. This table is analogous to table B 17, except that it is computed based on the values in C 16 (or C 13 if no trading day adjustment is requested).For more information, see X-11 Census Method II Seasonal Adjustment.

X11 output: C 18. Final Trading-day Factors Derived From Combined Daily Weights. ThisFor more information, see X-11 Census Method II Seasonal Adjustment.

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: D 1. Original Series Modified by Final Weights and Adjusted for Trading-day and Prior Variation. This X-11 table is analogous to C 1, except that the C 17 weights and C 19 adjusted series are used in the computations.For more information, see X-11 Census Method II Seasonal Adjustment.

X11 output: D 2. Trend-cycle. A 12-term moving average of D 1 is computed to estimate the trend-cycle component.For more information, see X-11 Census Method II Seasonal Adjustment.

X11 output: D 4. Modified S-I Differences (Ratios). The modified S-I differences (ratios) are computed by subtracting D 2 from (additive model) or dividing D 2 into (multiplicative model) the values in D 1.For more information, see X-11 Census Method II Seasonal Adjustment.

X11 output: D 5. Seasonal Factors. This X-11 table is computed analogously to B 5, except that the computations are based on the values in D 4.For more information, see X-11 Census Method II Seasonal Adjustment.

X11 output: D 6. Seasonally Adjusted Series. The values in this table are computed by subtracting D 5 from D 1 (additive model) or dividing D 1 by D5 (multiplicative model).For more information, see X-11 Census Method II Seasonal Adjustment.

X11 output: D 7. Trend-cycle. The values in thisFor more information, see X-11 Census Method II Seasonal Adjustment.

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: D 10. Final Seasonal Factors. ThisFor more information, see X-11 Census Method II Seasonal Adjustment.

X11 output: D 11. Final Seasonally Adjusted Series. The final seasonally adjusted series is computed by subtracting D 10 from C 19 (additive model) or dividing C 19 by D 10 (multiplicative model).For more information, see X-11 Census Method II Seasonal Adjustment.

X11 output: D 12. Final Trend-cycle. These values are computed by subtracting D 10 from D 1 (additive model), or by dividing D 1 by D 10 (multiplicative model).For more information, see X-11 Census Method II Seasonal Adjustment.

X11 output: D 13. Final Irregular. These values are computed by subtracting D 12 from D 11 (additive model), or by dividing D 11 by D 12 (multiplicative model).For more information, see X-11 Census Method II Seasonal Adjustment.

X11 output: E 1. Modified Original Series. The values in thisFor more information, see X-11 Census Method II Seasonal Adjustment.

X11 output: E 2. Modified Seasonally Adjusted Series. These values are computed by replacing in the final seasonally adjusted series (D 11) extreme values (identified by a zero weight in C 17) with the D 12 final trend-cycle values.For more information, see X-11 Census Method II Seasonal Adjustment.

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 thisFor more information, see X-11 Census Method II Seasonal Adjustment.

X11 output: E 6. Differences (Percent Changes) in Final Seasonally Adjusted Series. These values are the month-to-month (quarter-to-quarter) differences (additive model) or percent changes (multiplicative model) in D 11.For more information, see X-11 Census Method II Seasonal Adjustment.

X11 output: F 1. MCD (QCD) Moving Average. 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 componentFor more information, see X-11 Census Method II Seasonal Adjustment.

X11 output: F 2. Summary Measures. Several final summary- The average differences (additive model) or percent changes (multiplicative model) are computed without regard to sign across spans 1, 2, 3 ..., 12 months (or four quarters) for the following series: Original series A 1 (B 1), final seasonally adjusted series (D 11), final irregular series (D 13), final trend-cycle (D 12), final seasonal factors (D 10), final prior monthly adjustment factors (A 2, monthly
*X-11*only), final trading-day adjustment factors (C 18, monthly*X-11*only), modified original series (E 1), modified seasonally adjusted series (E 2), modified irregular series (E 3). - Next a table of relative contributions of the different components to the differences (additive model) or percent changes (multiplicative model) in the original series are computed.
- The next table reports the average duration of run (the average number of consecutive monthly changes in the same direction; "no change" is counted as a change in the same direction) for the following series: Final seasonally adjusted series (D 11), final irregular series (D 13), final trend-cycle (D 12), and the MCD (QCD) moving average (F 1).
- Finally, the means and standard deviations of differences (additive model) or percent changes (multiplicative model) are computed across different spans for each of the series mentioned above.

For more information, see X-11 Census Method II Seasonal Adjustment.

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)For more information, see X-11 Census Method II Seasonal Adjustment.

X11 output: G 3. Chart. This plot shows the same values as G 2; however, this line plot shows those values in chronological order.For more information, see X-11 Census Method II Seasonal Adjustment.

X11 output: G 4. Chart. This is a line graph of the final irregular and final modified irregular series (D 13 and E 3, respectively).For more information, see X-11 Census Method II Seasonal Adjustment.

Yates Corrected Chi-square. The approximation of the Chi-square statistic in small 2 x 2 tables can be improved by reducing the absolute value of differences between expected and observed frequencies by 0.5 before squaring (Yates' correction). This correction, which makes the estimation more conservative, is usually applied when the table contains only small observed frequencies, so that some expected frequencies become less than 10 (for further discussion of this correction, see Conover, 1974; Everitt, 1977; Hays, 1988; Kendall & Stuart, 1979; and Mantel, 1974).
Year 2000 Compatibility.
As we approach the end of this millennium, many users of data analysis software have discovered that their programs do not support dates with a
year designation that starts with any other digits but "19." Thus, effectively, that software is incompatible with the dates that will soon become a reality (and even now need to be used in modeling, forecasting, etc.). *STATISTICA* (see University site licenses) is one of very few programs that is not only "year-2000
compatible" but, also so-called, "year-2000-friendly" by offering flexible
options to customize the operation of the program (e.g., the interpretation
of ambiguous date designations, such as 1/1/20, where 20 could mean 1920 or
2020), to meet different specific needs of the data analysts.

STATISTICA is a trademark of StatSoft, Inc.