Search⌘ K
AI Features
Home
Courses
Time Series Analysis with Python

Holt-Winters

Understand the Holt-Winters method to apply exponential smoothing for time series forecasting. Learn how to model level, trend, and seasonality components with additive or multiplicative approaches. This lesson guides you to implement this technique in Python using the statsmodels package, preparing you to forecast data with clear seasonal and trend patterns.

We'll cover the following...

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 FtF_t is calculated as Ft=αxt+(1−α)Ft−1F_t = \alpha x_t + (1-\alpha) F_{t-1} for an additive model and as Ft=αxt(1−α)Ft−1F_t = \alpha x_t (1-\alpha) F_{t-1} for a multiplicative model in which α\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: ...