Understanding Holt-Winters

Past data is compressed using exponential smoothing via the Holt-Winters method to anticipate typical values for the present and the future. Exponential smoothing means smoothing a time series using an exponentially weighted moving average (EWMA). Like a rolling mean, it can be used on past data to make it smoother but also to make forecasts for future values.

An exponentially weighted moving average $F_t$ is calculated as $F_t = \alpha x_t + (1-\alpha) F_{t-1}$ for an additive model and as $F_t = \alpha x_t (1-\alpha) F_{t-1}$ for a multiplicative model in which $\alpha$ is a smoothing constant.

The Holt-Winters method includes both a slope smoothing component to take the trend into account and a seasonal smoothing. So the model gets three equations—one for the level, one for the trend, and one for seasonality. Furthermore, each of these three equations has two versions—additive and multiplicative.

Level
- Additive: ...

Introduction to Time Series

Python Basics for Time Series

Time Series Analysis

Basic Time Series Forecasting

Time Series Forecasting with Prophet in Python

Advanced Time Series Forecasting

Forecast Evaluation

Time Series Analysis and Forecasting

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Conclusion

Holt-Winters

Understanding Holt-Winters