STL: A Seasonal-Trend Decomposition Procedure Based on Loess

Robert B. Cleveland, William S. Cleveland, Jean E. McRae, and Irma Terpenning

Abstract:
STL is a filtering procedure for decomposing a time series into trend, seasonal, and remainder components. STL has a simple design that consists of a sequence of applications of the loess smoother; the simplicity allows analysis of the properties of the procedure and allows fast computation, even for very long time series and large amounts of trend and seasonal smoothing. Other features of STL are specification of amounts of seasonal and trend smoothing that range, in a nearly continuous way, from a very small amount of smoothing to a very large amount; robust estimates of the trend and seasonal components that are not distorted by aberrant behavior in the data; specification of the period of the seasonal component to any integer multiple of the time sampling interval greater than one; and the ability to decompose time series with missing values.

Keywords:
Seasonal adjustment; time series; loess.