Exponential Smoothing (Holt-Winters)

Holt-Winters exponential smoothing forecasts a time series by updating exponentially weighted estimates of its level, trend, and seasonal components, with seasonality treated as additive or multiplicative.

홀트-윈터스 지수평활법은 시계열의 수준, 추세, 계절 성분을 지수적으로 가중한 추정치로 갱신하여 예측하며, 계절성은 가법형 또는 승법형으로 다룹니다.

How do I forecast a time series that has both a trend and a seasonal pattern?

추세와 계절성이 함께 있는 시계열은 어떻게 예측하나요?

Holt-Winters exponential smoothing produces forecasts by giving more weight to recent observations while tracking a series' level, trend, and seasonality. It fits regularly spaced series with a stable seasonal pattern, using additive seasonality when seasonal swings are constant and multiplicative seasonality when they grow with the level.

When to use Exponential Smoothing (Holt-Winters)

• Monthly or quarterly sales, demand, or visitor counts with a seasonal cycle
• Short- to medium-term forecasting of a single series
• Series with a stable trend and a known seasonal period

When to use something else

• Autocorrelation structure or external predictors matter: use ARIMA or SARIMAX
• Multiple or complex seasonal patterns: use TBATS or a dynamic harmonic regression

Assumptions and requirements

• Regularly spaced observations with no gaps
• Known seasonal period
• At least two full seasonal cycles for initialization
• Seasonal pattern reasonably stable over time

What the analysis reports

• Smoothing parameters (alpha, beta, gamma)
• Point forecasts with prediction intervals
• Fitted versus actual plot
• Accuracy measures such as RMSE, MAE, and MAPE
• AIC for comparing model variants

How to report it

An additive Holt-Winters model (α = [value], β = [value], γ = [value]) produced a holdout MAPE of [value]%.

Related methods

• ARIMA
• Simple Exponential Smoothing
• Seasonal Decomposition (STL)

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