“The Exponential Smoothing technique is a powerful forecasting method that applies exponentially decreasing weights to past observations. This method prioritizes recent information, making it significantly more responsive than SMAs to sudden shifts.” – Simple exponential smoothing (SES) –
Simple Exponential Smoothing (SES) is the simplest form of exponential smoothing, a time series forecasting method that applies exponentially decreasing weights to past observations, prioritising recent data to produce responsive forecasts for series without trend or seasonality.1,2,3,5
Core Definition and Mechanism
SES generates point forecasts by recursively updating a single smoothed level value, (\ellt), using the formula:
\ell</em>t = \alpha y<em>t + (1 - \alpha) \ell</em>{t-1}
where (yt) is the observation at time (t), (\ell{t-1}) is the previous level, and (\alpha) (0 < (\alpha) < 1) is the smoothing parameter controlling the weight on the latest observation.1,2,3,5 The forecast for all future periods is then the current level: (\hat{y}{t+h|t} = \ellt).5
Unrolling the recursion reveals exponentially decaying weights:
\hat{y}<em>{t+1} = \alpha \sum</em>{j=0}^{t-1} (1 - \alpha)^j y<em>{t-j} + (1 - \alpha)^t \ell</em>1
Recent observations receive higher weights ((\alpha) for the newest), forming a geometric series that decays rapidly, making SES more reactive to changes than simple moving averages (SMAs).1,3 Initialisation typically estimates (\alpha) and (\ell_1) by minimising loss functions like SSE.1,3
Key Properties and Applications
- Parameter Interpretation: High (\alpha) (near 1) emphasises recent data, ideal for volatile series; low (\alpha) (near 0) acts like a global average, filtering noise in stable series.1,2
- Assumptions: Best for stationary data without trend or seasonality; extensions like ETS(A,N,N) address limitations via state-space models.1,4,5
- Implementation: Widely available in libraries (e.g.,
smooth::es()in R,statsmodels.tsa.SimpleExpSmoothingin Python).1,2 - Advantages: Simple, computationally efficient, intuitive for practitioners.1,5 Limitations include point forecasts only (no native intervals pre-state-space advances).1
Examples show SES tracking level shifts effectively with moderate (\alpha), outperforming naïve methods on non-trending data.1,5
Best Related Strategy Theorist: Robert Goodell Brown
Robert G. Brown (1925–2023) is the pioneering theorist most closely linked to SES, having formalised exponential smoothing in his seminal 1956 work Statistical Forecasting for Inventory Control, where he introduced the recursive formula and its inventory applications.1,3
Biography: Born in the US, Brown earned degrees in physics and engineering, serving in the US Navy during WWII on radar and signal processing—experience that shaped his interest in smoothing noisy data.3 Post-war, at the Naval Research Laboratory and later industry roles (e.g., Autonetics), he tackled operational forecasting amid Cold War demands for efficient supply chains. His 1959 book Statistical Forecasting for Inventory Control popularised SES for business, proving it minimised stockouts via weighted averages. Brown’s innovations extended to double and triple smoothing for trends/seasonality, influencing ARIMA and modern ETS frameworks.1,3,5 Collaborations with Charles Holt (Holt-Winters) cemented his legacy; he consulted for firms like GE, authoring over 50 papers. Honoured by INFORMS, Brown’s practical focus bridged theory and strategy, making SES a cornerstone of demand forecasting in supply chain management.3
References
1. https://openforecast.org/adam/SES.html
2. https://www.influxdata.com/blog/exponential-smoothing-beginners-guide/
3. https://en.wikipedia.org/wiki/Exponential_smoothing
4. https://nixtlaverse.nixtla.io/statsforecast/docs/models/simpleexponentialsmoothing.html
5. https://otexts.com/fpp2/ses.html
6. https://qiushiyan.github.io/fpp/exponential-smoothing.html
