STL Decomposition

STL decomposition splits a time series into trend, seasonal and remainder components using iterated LOESS smoothing, optionally with robustness weights that limit the influence of outliers.

STL 분해는 반복 LOESS 평활로 시계열을 추세·계절·잔차 성분으로 나누는 방법으로, 이상치의 영향을 줄이는 강건 가중치를 쓸 수 있다.

How can I separate the trend and the seasonal pattern in my monthly visitor counts?

월별 방문객 수에서 추세와 계절 패턴을 따로 떼어 보고 싶어요.

STL fits the seasonal component by smoothing each cycle position across years and the trend by smoothing the deseasonalised series, repeating until stable. Trend and seasonal strength measures summarise how much of the variation each component explains relative to the remainder.

When to use STL Decomposition

• The series has a regular seasonal period such as 12 months or 4 quarters.
• The seasonal pattern may change slowly over time.
• Outliers are present and you want a robust decomposition.

When to use something else

• The seasonal swing grows with the level and you do not want to log-transform; use multiplicative Seasonal Decomposition instead.
• There is no fixed period or several interacting periods; use Spectral Analysis (Periodogram) to find the cycles first.

Assumptions and requirements

• Additive structure: observed = trend + seasonal + remainder.
• A known seasonal period with at least two full cycles.
• Equally spaced observations without gaps.

What the analysis reports

• Trend, seasonal and remainder series
• Trend strength and seasonal strength (0–1)
• Seasonal amplitude
• Remainder standard deviation

How to report it

An STL decomposition (period = [value]) showed a trend strength of [value] and a seasonal strength of [value].

Related methods

• Seasonal Decomposition
• Hodrick-Prescott Filter
• Exponential Smoothing (Holt-Winters)

Run STL Decomposition on Quorant