I am learning about time series decomposition using the X-11 method in R. I am following the book “Forecasting: Principles and Practice (3rd ed)” by Rob J Hyndman and George Athanasopoulos, which uses the seasonal package to perform seasonal adjustment.

I have a question about the seasonal component obtained from the X-11 method. I applied the X-11 method to the us_retail_employment data, which is available in the fpp3 package. The code and the plot are shown below:

https://otexts.com/fpp3/x11.html

As you can see, the seasonal component shows a decreasing trend in amplitude and peaks after January 2010, even though the original data shows an increasing trend in employment. This seems counterintuitive to me, as I would expect the seasonal component to reflect the seasonal patterns in the data.

I am wondering why this inconsistency occurs and how to interpret it. Is it due to the choice of the X-11 method over the SEATS method? Is it due to some features or assumptions of the X-11 method that affect the seasonal component estimation? Is it due to some characteristics of the data that make the seasonal component change over time?

Thank you for your help and insights.