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

Default → None

Smoothing parameter for the trend.
gamma

Default → None

Smoothing parameter for the seasonality.
seasonality

Default → 0

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

Default → 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 — 'list[dict] | None' — defaults to None

learn_one

Updates the model.

Parameters

y — 'float'
x — 'dict | None' — defaults to None