Time Series Forecasting • Statistical Models (ARIMA, Exponential Smoothing)Medium⏱️ ~3 min
Exponential Smoothing: Level, Trend, and Seasonal Components
Exponential Smoothing (ETS) models represent a time series as latent components: level, trend, and seasonality. Each component updates recursively using smoothing parameters that control how quickly the model responds to new observations. Simple Exponential Smoothing tracks only a level component. Holt's method adds a linear trend. Holt Winters extends this with seasonality in either additive or multiplicative forms.
The choice between additive and multiplicative seasonality depends on the amplitude pattern. Additive seasonality means seasonal fluctuations stay constant regardless of the level: holiday sales might always increase by 1000 units. Multiplicative seasonality means fluctuations scale with the level: holiday sales might increase by 20 percent. For example, Amazon forecasting demand for high volume items would use multiplicative seasonality because a popular item selling 10,000 units daily sees a 2,000 unit holiday bump, while a niche item selling 100 units sees only a 20 unit bump.
Modern state space formulations enable probabilistic forecasting with uncertainty intervals and support online updates in constant time per observation. This is critical at scale: Uber forecasting demand for 5,000 zones can update each zone's forecast in 1 to 5 milliseconds per new data point, keeping p95 latencies below 20 milliseconds. Unlike ARIMA, ETS does not require stationarity or differencing because it models structure directly through component recursions.
The computational advantage is substantial. A retailer forecasting 20 million item location series can complete batch updates in 90 minutes using 2,000 cores, with each series fitting in approximately 250 milliseconds. The constant time update property means streaming implementations scale linearly: doubling the number of series doubles compute needs but does not change per series latency.
💡 Key Takeaways
•ETS models decompose time series into level, trend, and seasonal components that update recursively with each new observation
•Additive seasonality suits constant amplitude fluctuations (plus or minus 1000 units), multiplicative suits proportional fluctuations (plus or minus 20 percent)
•State space formulation enables constant time O(1) updates per observation, supporting real time streaming at 1 to 5 milliseconds per series
•Production scale: 20 million series forecasts complete in 90 minutes on 2,000 cores at 250 milliseconds per series fit
•No stationarity requirement: ETS models components directly without differencing, making it more robust than ARIMA for nonstationary data
•Uber uses ETS for minute level zone demand forecasts updating every 1 to 5 minutes with p95 latency under 100 milliseconds across thousands of zones
📌 Examples
Amazon item location forecasting: multiplicative seasonality for high volume items where holiday sales increase by 20 percent rather than a fixed amount
Netflix CDN capacity planning: ETS forecasts viewing load per region for 1 to 7 day horizons with target MAPE under 10 percent for high volume regions
Uber zone demand: streaming ETS updates every minute with p95 update latency under 20 milliseconds per zone to feed surge pricing control loops