Statistical Details for X-11 Decomposition
This method adjusts the original time series using either a multiplicative or an additive decomposition. The model is fit using an iterative process to estimate the three X-11 components: trend cycle, seasonal, and irregular. The trend cycle component contains both the long-term trend and the long-term cyclical effects. The irregular component contains the effects of variation unexplained by the trend and seasonal components. For a historical overview of the development of the X-11 method, see SAS/ETS 15.2 User’s Guide (search for “Historical Development of X-11”).
The multiplicative adjustment fits the following model:
where
Ot is the original time series
Ct is the trend cycle component
St is the seasonal component
It is the irregular component
The adjusted multiplicative trend is Ot /St.
The additive adjustment fits the following model:
The adjusted additive trend is Ot - St.