Michael Brenndoerfer | Data & AI, Private Equity, Technology

Michael Brenndoerfer

ETS (Exponential Smoothing) › Visualizing Exponential Smoothing

Michael BrenndoerferAugust 8, 20255 min read

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Chapter 57ETS (Exponential Smoothing) › Visualizing Exponential Smoothing

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Let's create visualizations that demonstrate how exponential smoothing works with different parameter values and time series patterns.

Out[7]:

Visualization

Time series plot showing how different alpha values affect exponential smoothing responsiveness. — This visualization shows how different smoothing parameters (α) affect the responsiveness of exponential smoothing to recent changes. Higher α values (0.9) make the forecast more responsive to recent observations, while lower α values (0.1) create smoother forecasts that change more slowly. The optimal α value depends on the noise level and how quickly the underlying pattern changes.

Now let's visualize how exponential smoothing handles different types of time series patterns:

Out[8]:

Visualization

Time series plot showing exponential smoothing adapting to changing trends. — This shows how exponential smoothing adapts to a time series with a changing trend. The method gradually adjusts to the new trend direction, with the adaptation speed controlled by the smoothing parameter. The forecast follows the trend while smoothing out random fluctuations.

Time series plot showing exponential smoothing handling seasonal patterns. — This demonstrates exponential smoothing applied to seasonal data. The method captures the seasonal pattern while adapting to changes in the seasonal amplitude over time. The forecast maintains the seasonal structure while smoothing out noise.

Let's also visualize the weight structure of exponential smoothing:

Out[9]:

Visualization

Bar chart showing exponential decay of weights for different time periods in exponential smoothing. — This visualization shows the exponential decay of weights in exponential smoothing. Each bar represents the weight given to an observation from a specific time period in the past. The weights decrease exponentially as we go further back in time, with the most recent observation receiving the highest weight. Different α values create different decay patterns, with higher α values giving more weight to recent observations.