Exponential Smoothing Models#

Stage 6 · 🏗️ Building & Forecasting Models · Lesson 18 of 18 · advanced

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The idea#

Exponential smoothing forecasts with a weighted average of past observations, where the weights decay exponentially into the past — recent data counts most, older data fades but never fully vanishes. It is a different lineage from ARIMA, built around components (level, trend, season) rather than autocorrelations.

Simple smoothing#

The simplest form, Simple Exponential Smoothing (SES), tracks a single level and suits series with no trend or seasonality:

\[\hat{x}_{t+1} = \alpha\, x_t + (1 - \alpha)\, \hat{x}_t, \qquad 0 < \alpha < 1.\]

The smoothing parameter \(\alpha\) sets the memory: near 1 reacts fast to recent values, near 0 stays smooth and sluggish. Its forecasts are flat.

Adding trend and season#

Two extensions handle richer data. Holt’s linear method adds a trend component (a second parameter \(\beta\)), giving sloped forecasts. Holt–Winters adds a seasonal component too (a third parameter \(\gamma\)), either additive or multiplicative — the standard choice for series with both trend and seasonality. Together these form the ETS (Error–Trend–Seasonal) family.

Smoothing or ARIMA?#

The two approaches are complementary, not rivals: ARIMA describes a series through its autocorrelations, exponential smoothing through its trend and seasonal structure. Which wins is empirical — smoothing often shines on strongly trended, seasonal data, ARIMA on stationary, mean-reverting data. In statsmodels these live in SimpleExpSmoothing, Holt and ExponentialSmoothing (Holt–Winters).

Hint