ETS: Error, Trend, Seasonal Exponential Smoothing
Error, Trend, Seasonal (ETS) Exponential Smoothing · Also known as: exponential smoothing state space model, innovations state space model, Holt-Winters family, ETS — Hata/Trend/Mevsimsellik Üstel Düzleştirme
ETS is a comprehensive exponential smoothing framework that automatically selects additive or multiplicative combinations of the error (E), trend (T) and seasonal (S) components of a time series. Formalised as an innovations state space model by Hyndman, Koehler, Ord and Snyder in 2008, it unifies and generalises the Holt-Winters family of forecasting methods.
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When to use it
Use ETS for forecasting a single continuous time series that is recorded at regular intervals and shows level, trend and/or seasonal structure, with at least about 24 observations (roughly two seasonal cycles). It assumes regular time series data whose components can be decomposed additively or multiplicatively, but it does not require normality. It is well suited to automatic, robust short-to-medium horizon forecasting; it is less appropriate for irregular series, very short histories, or problems that need explanatory predictors.
Strengths & limitations
- Automatically searches additive and multiplicative error, trend and seasonal specifications and selects the best by an information criterion.
- Encompasses the whole Holt-Winters family as special cases within one consistent state space framework.
- Robust, fast automatic forecasting that does not require the data to be normally distributed.
- Needs at least about 24 observations, roughly two full seasonal cycles, to estimate the components reliably.
- Requires a regular time series whose components are decomposable; it handles only a single series and cannot use explanatory variables.
- Multiplicative specifications are undefined or unstable when the series contains zero or negative values.
Frequently asked
What do the three ETS letters mean?
They label the error, trend and seasonal components. Each can be 'N' (none), 'A' (additive) or 'M' (multiplicative); for example ETS(A,A,A) is additive throughout, while ETS(M,A,M) combines a multiplicative error and seasonality with an additive trend. The automatic procedure can try the 'Z' (auto) setting for each letter.
How is ETS related to Holt-Winters?
Holt-Winters triple exponential smoothing is a special case of ETS. The ETS framework contains the entire Holt-Winters family and adds principled likelihood estimation, automatic selection and prediction intervals through its state space formulation.
When should I prefer additive over multiplicative seasonality?
Use additive seasonality when the seasonal swings stay roughly constant in size as the level rises, and multiplicative seasonality when the swings grow in proportion to the level. Multiplicative forms require strictly positive data.
How much data does ETS need?
At least about 24 observations, which is roughly two complete seasonal cycles for monthly data, so that the level, trend and seasonal components can be separated and estimated reliably.
Sources
- Hyndman, R. J., Koehler, A. B., Ord, J. K. & Snyder, R. D. (2008). Forecasting with Exponential Smoothing: The State Space Approach. Springer. DOI: 10.1007/978-3-540-71918-2 ↗
- Hyndman, R. J. & Athanasopoulos, G. (2021). Forecasting: Principles and Practice (3rd ed.). OTexts. link ↗
How to cite this page
ScholarGate. (2026, June 1). Error, Trend, Seasonal (ETS) Exponential Smoothing. ScholarGate. https://scholargate.app/en/econometrics/ets-model
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
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