Combined seasonality test

This test combines the Kruskal-Wallis test along with test for the presence of seasonality assuming stability ($F_{S}$), and evaluative seasonality test for detecting the presence of identifiable seasonality ($F_{M}$). Those three tests are calculated using the final unmodified SI component. The main purpose of the combined seasonality test is to check whether the seasonality of the series is identifiable. For example, the identification of the seasonal pattern is problematic if the process is dominated by highly moving seasonality¹. The testing procedure is shown in the figure below.

Combined seasonality test, source: LADIRAY, D., QUENNEVILLE, B. (2001)