Wrong number of differences in QS test?

[Luis-Sanguiao]

We observed differences between TRAMO-SEATS and JDemetra+ in the QS statistic (specially for the SA series), and we realized that it was because the number of regular differences taken (this is found in diagnostics -> seasonality tests). JDemetra+ seems to difference once even for models with one regular plus one seasonal difference.

According to "Detecting Seasonality in Seasonally Adjusted Monthly Time Series" (Findley, Lytras, McElroy 2017) page 21, two differences should be taken when the ARIMA model of the unadjusted series has both a seasonal and a nonseasonal differencing (which is by far the more common scenary). TRAMO-SEATS, on the other hand, seems to take two differences in those cases. We checked this with the tool Seasonality Test of JDemetra+: taking two differences lead to the same QS statistic as TRAMO-SEATS.

Underdifferencing the series, is likely to detect false evidences of residual seasonality. We conclude that JDemetra+ should adjust the number of differences taken for the QS test according to the series analysed.

Thank you