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exponential smoothing

nounAlso: Holt–Winters method, Holt's linear trend method, simple exponential smoothing, ETS

In plain wordsA simple forecasting method that predicts the next value as a weighted average of past values, giving the most weight to recent ones and steadily less to older ones.

  1. A family of time series forecastingtime series forecasting, n.: Predicting future values of something measured over time, such as sales, electricity demand, prices or rainfall, from its past values and related information. methods built on recursive blending: each period the current estimate is nudged toward the newest observation, so every past value still counts but its influence shrinks geometrically as it ages. Simple exponential smoothing keeps a single smoothed level, updated each period as α times the new observation plus (1 − α) times the previous level, where the smoothing parameter α lies between 0 and 1; Holt's method adds a trend component, and the Holt–Winters method adds seasonality in additive or multiplicative form, with damped-trend variants that flatten long-range forecasts. Since the early 2000s these methods have been formulated as innovations state-space models, labeled ETS (error, trend, seasonal), which supply likelihoods for automatic model selection and proper prediction intervals. Cheap, robust and hard to beat on short or noisy series, exponential smoothing remains a standard baselinebaseline, n.: A simple reference method that a new model must beat to show it is worth anything, such as always guessing the most common answer or reusing yesterday's value. and a production workhorse for demand and inventory forecasting at scale.

    For the 40,000 slow-moving spare parts we simply use damped Holt–Winters exponential smoothing.

ℓt=α yt+(1−α) ℓt−1,y^t+1∣t=ℓt\ell_t = \alpha\, y_t + (1 - \alpha)\, \ell_{t-1}, \qquad \hat{y}_{t+1 \mid t} = \ell_t

Origin

Developed for inventory control and military logistics in the 1950s: Robert G. Brown, an operations researcher who first used it in U.S. Navy work, presented it for forecasting inventory demand in 1956; Charles Holt added trend (1957) and Peter Winters added seasonality (1960). Rob Hyndman and colleagues gave the methods a statistical state-space foundation in 2002 and in a 2008 book.

Related

See also
  • time series forecastingtime series forecasting, n.: Predicting future values of something measured over time, such as sales, electricity demand, prices or rainfall, from its past values and related information.
  • ARIMAARIMA, n.: A classic statistical recipe for forecasting a series of numbers over time: remove any steady trend, then predict the next value from recent values and recent prediction errors.
  • baselinebaseline, n.: A simple reference method that a new model must beat to show it is worth anything, such as always guessing the most common answer or reusing yesterday's value.
  • exponential moving average of weightsexponential moving average of weights, n.: A smoothed copy of a model kept during training, which each update nudges only slightly toward the latest weights. The calmer copy often performs better than the jittery original.

Sources

  1. Holt, C. C. (1957). Forecasting Seasonals and Trends by Exponentially Weighted Moving Averages. ONR Memorandum 52; reprinted in International Journal of Forecasting 20(1), 2004.
  2. Winters, P. R. (1960). Forecasting Sales by Exponentially Weighted Moving Averages. Management Science 6(3).
  3. Hyndman, R. J., Koehler, A. B., Ord, J. K. & Snyder, R. D. (2008). Forecasting with Exponential Smoothing: The State Space Approach. Springer.

Mentioned in

ARIMAARIMA, n.: A classic statistical recipe for forecasting a series of numbers over time: remove any steady trend, then predict the next value from recent values and recent prediction errors., time series forecastingtime series forecasting, n.: Predicting future values of something measured over time, such as sales, electricity demand, prices or rainfall, from its past values and related information., time series foundation modeltime series foundation model, n.: A large AI model pretrained on huge numbers of time series, such as sales, traffic and sensor readings, that can forecast a new series it has never seen without being trained on it.