HoltWinters

Holt-Winters forecaster.

This is a standard implementation of the Holt-Winters forecasting method. Certain parametrisations result in special cases, such as simple exponential smoothing.

Optimal parameters and initialisation values can be determined in a batch setting. However, in an online setting, it is necessary to wait and observe enough values. The first k = max(2, seasonality) values are indeed used to initialize the components.

Level initialization

\[l = \frac{1}{k} \sum_{i=1}{k} y_i\]

Trend initialization

\[t = \frac{1}{k - 1} \sum_{i=2}{k} y_i - y_{i-1}\]

Trend initialization

\[s_i = \frac{y_i}{k}\]

Parameters

• alpha

  Smoothing parameter for the level.

• beta – defaults to None

  Smoothing parameter for the trend.

• gamma – defaults to None

  Smoothing parameter for the seasonality.

• seasonality – defaults to 0

  The number of periods in a season. For instance, this should be 4 for quarterly data, and 12 for yearly data.

• multiplicative – defaults to False

  Whether or not to use a multiplicative formulation.

Examples

>>> from river import datasets
>>> from river import metrics
>>> from river import time_series

>>> dataset = datasets.AirlinePassengers()

>>> model = time_series.HoltWinters(
...     alpha=0.3,
...     beta=0.1,
...     gamma=0.6,
...     seasonality=12,
...     multiplicative=True
... )

>>> metric = metrics.MAE()

>>> time_series.evaluate(
...     dataset,
...     model,
...     metric,
...     horizon=12
... )
+1  MAE: 25.899087
+2  MAE: 26.26131
+3  MAE: 25.735903
+4  MAE: 25.625678
+5  MAE: 26.093842
+6  MAE: 26.90249
+7  MAE: 28.634398
+8  MAE: 29.284769
+9  MAE: 31.018351
+10 MAE: 32.252349
+11 MAE: 33.518946
+12 MAE: 33.975057

Methods

forecast

Makes forecast at each step of the given horizon.

Parameters

• horizon ('int')
• xs ('typing.Optional[list[dict]]') – defaults to None

learn_one

Updates the model.

Parameters

• y ('float')
• x ('dict') – defaults to None

References

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1. Exponential smoothing — Wikipedia ↩

2. Exponential smoothing — Forecasting: Principles and Practice ↩

3. What is Exponential Smoothing? — Engineering statistics handbook ↩