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Specifically, I found the reference in the SAS PROC X11 documentation pages, and am curious what the modifier "identifiable" means in this context. Thanks!


Additional context from the link based on comments:

The seasonal component of this time series, $s_t$, is defined as the intrayear variation that is repeated constantly (stable) or in an evolving fashion from year to year (moving seasonality). If the increase in the seasonal factors from year to year is too large, then the seasonal factors will introduce distortion into the model. It is important to determine if seasonality is identifiable without distorting the series.

To determine if stable seasonality is present in a series, PROC X11 computes a one-way analysis of variance by using the seasons (months or quarters) as the factor on the Final Unmodified SI Ratios (Table D8). This is the appropriate table to use because the removal of the trend cycle is equivalent to detrending. PROC X11 prints this test, labeled "Stable Seasonality Test," immediately after the Table D8.

The X11 seasonal adjustment method tests for moving seasonality. Moving seasonality can be a source of distortion when seasonal factors are used in the model. PROC X11 computes and prints a test for moving seasonality. The test is a two-way analysis of variance that uses months (or quarters) and years. As in the "Stable Seasonality Test," this analysis of variance is performed on the Final Unmodified SI Ratios (Table D8). PROC X11 prints this test, labeled "Moving Seasonality Test," after the "Stable Seasonality Test."

PROC X11 next computes a nonparametric Kruskal-Wallis chi-squared test for stable seasonality, "Nonparametric Test for the Presence of Seasonality Assuming Stability." The Kruskal-Wallis test is performed on the ranks of the Final Unmodified SI Ratios (Table D8). For further details about the Kruskal-Wallis test, see Lehmann (1998, pp. 204–210).

The results of the preceding three tests are combined into a joint test to measure identifiable seasonality, "Summary of Results and Combined Test for the Presence of Identifiable Seasonality." This test combines the two F tests previously described, along with the Kruskal-Wallis chi-squared test for stable seasonality, to determine "identifiable" seasonality. This test is printed after "Nonparametric Test for the Presence of Seasonality Assuming Stability."

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    $\begingroup$ It would help to explain the salient points from the link as links go dead all the time and this Q&A should be sustainable even if the link were to die. Without going to the site it is difficult to know to what extent this is or is not a statistical question. $\endgroup$ – Gavin Simpson Mar 2 '15 at 20:10
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    $\begingroup$ Note that asking about how to use SAS is off-topic here, but this may be a statistical (not software) question. In light of @GavinSimpson's points, can you clarify what you are asking about & maybe paste in whatever context is required for the Q to stand on its own? $\endgroup$ – gung Mar 2 '15 at 20:17
  • $\begingroup$ Good points, both of you. I added a quote from the link, but it is difficult to explain the question without answering it now that I've read the definition provided in the accepted answer. $\endgroup$ – Sean W. Mar 2 '15 at 22:46
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From Statistics Canada, Seasonal adjustment and trend-cycle estimation:

Identifiable seasonality is defined as a seasonal pattern that is not obscured by a high degree of irregular fluctuations and thus can be identified reliably (Lothian and Morry, 1978).

The paper cited for this definition is:

Lothian, J. and Morry, M. (1978). A test for the presence of identifiable seasonality when using the X-11 program. Research paper 78-10-002E, Seasonal Adjustment and Time Series Staff, Statistics Canada.

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