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:
library(fpp3)
us_retail_employment <- us_employment |>
filter(year(Month) >= 1990, Title == "Retail Trade") |>
select(-Series_ID)
x11_dcmp <- us_retail_employment |>
model(x11 = X_13ARIMA_SEATS(Employed ~ x11())) |>
components()
autoplot(x11_dcmp) +
labs(title =
"Decomposition of total US retail employment using X-11.")
it generates the the following image:
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?
I am also interested in learning more about the inner workings of the X-13ARIMA-SEATS function and how it calculates the seasonal component. I have read the reference manual and the R documentation, but I still find them quite complex and technical. I would appreciate it if someone could explain in simple terms how the X-13ARIMA-SEATS function works and what steps it takes to perform seasonal adjustment.
Thank you for your help and insights.
