STL Decomposition: Seasonal-Trend Decomposition using Loess
STL: Seasonal-Trend Decomposition using Loess · Also known as: Seasonal-Trend Decomposition using Loess, STL filtering, Loess-based seasonal decomposition, Mevsimsel-Trend Ayrıştırma (STL)
STL Decomposition, introduced by Cleveland, Cleveland, McRae, and Terpenning (1990), is a nonparametric procedure that separates a time series into three additive components — trend, seasonal, and remainder — using iterative locally weighted regression (loess). Widely used in economics, meteorology, and data science, it handles time series of any periodicity and is robust to the presence of outliers, making it a highly flexible alternative to classical decomposition methods.
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When to use it
Use STL when you have a univariate time series with a clear seasonal pattern and want component estimates that are robust to outliers and allow the seasonal shape to change over time. It suits monthly, quarterly, weekly, or any fixed-periodicity data. Key assumptions: the series is approximately additive (use a log transform first if multiplicative); the period length is known and fixed. STL does not produce calendar adjustments or confidence intervals natively. For official statistical releases with trading-day and holiday effects, X-13ARIMA-SEATS is preferred. For short series or ARIMA-based inference, classical decomposition or ARIMA models may be more appropriate.
Strengths & limitations
- Handles any periodicity (weekly, monthly, quarterly) without modification
- Allows the seasonal component to change gradually over time
- Robust outer loop reduces sensitivity to outliers and structural breaks
- Simple, interpretable additive decomposition with user-controlled smoothing bandwidths
- Assumes an additive structure; multiplicative seasonality requires a prior log transformation
- Does not automatically adjust for trading-day effects, holidays, or calendar variation
- Bandwidth parameters (seasonal and trend windows) must be chosen by the analyst and affect results materially
- Provides no formal statistical inference or confidence intervals for the estimated components
Frequently asked
How do I choose the seasonal and trend window parameters?
Cleveland et al. (1990) recommend starting with the smallest odd integer greater than 1.5 times the period for the seasonal window and an odd integer that yields a smooth trend relative to the data length. In practice, analysts compare decompositions across several bandwidth values and select those where the remainder appears structureless. No single automatic rule fits all series, so diagnostic inspection of the remainder is essential.
Can STL handle multiple seasonal periods, such as daily and weekly patterns?
The original STL procedure handles one fixed period at a time. For multiple seasonalities — for example, hourly data with both daily and weekly cycles — extensions such as MSTL (Multiple STL) or STR apply the loess framework iteratively across each seasonal period. These extensions are available in R and Python and follow the same iterative logic as the original Cleveland et al. method.
Is STL suitable for forecasting?
STL itself is a decomposition procedure, not a forecasting model. However, it is routinely used as a pre-processing step: the trend and seasonal components are extrapolated separately (e.g., using exponential smoothing or ARIMA on the seasonally adjusted series) and then recombined. The STL+ETS combination is a common benchmark in forecasting competitions and operational forecasting workflows.
Sources
- Cleveland, R. B., Cleveland, W. S., McRae, J. E., & Terpenning, I. (1990). STL: A seasonal-trend decomposition procedure based on loess. Journal of Official Statistics, 6(1), 3–73. link ↗
How to cite this page
ScholarGate. (2026, June 2). STL: Seasonal-Trend Decomposition using Loess. ScholarGate. https://scholargate.app/en/econometrics/stl-decomposition
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