Question about X11

[timduy]

just want to make sure I am interpreting the tests within the x11 procedure correctly. It is my understanding that the null hypothesis in the stable and moving seasonality tests is "no season effects" are present. So if we have data with season effects, we should be rejecting the null, such as:

Code: Select all

                             Stable Seasonality Test
                        Sum of        Degrees of          Mean
                       Squares          Freedom          Square
Between Periods         0.000079               3           0.000026
Residual                0.000374             129           0.000003
Total                   0.000453             132

F-Ratio         9.07832    Significance Level (P)  0.0000170
Nonparametric Test for the Presence of Seasonality Assuming Stability
KW Statistic 21.585016 DOF 3 P-level 0.000080
                             Moving Seasonality Test
                        Sum of        Degrees of          Mean
                       Squares          Freedom          Square
Between Years         0.000060              32           0.000002
Error                 0.000115              96           0.000001

F-Ratio         1.55987    Significance Level (P)  0.0510248D9. Final replacement values for SI ratios

Is this the correct interpretation? And, second question, is there a defined variable that retains the test statistics/significance levels? From the documentation I think the answer is "no."

Thank you

[TomDoan]

No, it's a test for stable as opposed to moving seasonality. Basically, it's a test for whether seasonal dummies are adequate. Seasonal dummies, of course, will be adequate if there is no seasonality at all, but even fairly extreme seasonality will also pass if it's quite similar from year to year.

[timduy]

Tom:

Thank you. So is this:

https://ec.europa.eu/eurostat/sa-elearn ... ality-test

not interpreting the tests properly or are these different tests?

Thank you,

Tim

[TomDoan]

Upon further review, it's an ANOVA test (done on the data with the trend/cycle removed) for dummies for the seasonals. (Effectively, run a regression on constant and 11 seasonal dummies and do the F test on the dummies). So the null is that there is no difference between the months. If there is seasonality (even if moving) that would probably reject unless it moves in such a way that it flips signs over the course of the sample, which is unlikely in practice.

[timduy]

Ok. Thank you for the update!

Also, this footnote:

4. X-12-ARIMA is seasonal adjustment software developed by the United States Census Bureau. See the Census's "FAQ on Seasonal Adjustment" for a general overview of seasonal adjustment. The three standard tests (in X-12 ARIMA's table D8 A) for seasonality are: an F-test for stable seasonality (basically a Chi-square test under the null hypothesis that the average deviations from trend for the series for each quarter are equal); the Kruskal-Wallis non-parametric test (which tests whether the average rank of the observations for each quarter are different); and an F-test for moving seasonality. Note these statistical tests do not focus specifically on the first quarter but look for a regular pattern relating to the calendar. Also, the tests are designed to provide a check for seasonality in series that have not already been seasonally adjusted, and are just indicative of residual seasonality issues for series that have already been adjusted. Return to text

https://www.federalreserve.gov/econresd ... 4.html#fn3