Skip to content

PolynomialTrendForecaster

yohou.stationarity.trend.PolynomialTrendForecaster

Bases: _BaseTrendForecaster

Forecast using polynomial trend extrapolation with ElasticNet regularization.

Fits a polynomial of specified degree to the historical data using ElasticNet regression and extrapolates into the future. Linear trend is the special case with degree=1.

Parameters

Name Type Description Default
degree int

Polynomial degree. degree=1 gives linear trend, degree=2 quadratic, etc. Higher degrees can overfit - typically use degree <= 3.

 1
estimator RegressorMixin

Regression model used to fit polynomial coefficients.

 ElasticNet()
target_transformer BaseTransformer

Transformer for target variable (e.g., LogTransformer).

 None
panel_strategy ('global', multivariate)

How to handle panel data. See BaseForecaster for details.

 "global"

Attributes

Name Type Description
Fitted sklearn Pipeline with a polynomial feature transformer and the provided

a clone of the estimator model.

Examples

>>> import polars as pl
>>> from datetime import datetime
>>> from yohou.stationarity import PolynomialTrendForecaster
>>>
>>> # Create time series with linear trend
>>> y = pl.DataFrame({
...     "time": pl.datetime_range(
...         start=datetime(2020, 1, 1), end=datetime(2020, 12, 31), interval="1d", eager=True
...     ),
...     "value": range(366),
... })
>>>
>>> # Fit linear trend forecaster
>>> forecaster = PolynomialTrendForecaster(degree=1)
>>> forecaster.fit(y, forecasting_horizon=7)
PolynomialTrendForecaster()
>>>
>>> # Forecast next 7 days
>>> y_pred = forecaster.predict(forecasting_horizon=7)

See Also

Notes

  • For exponential trends, consider using target_transformer=LogTransformer() with degree=1
  • Polynomial trends can overfit - use with caution (typically degree <= 3)
  • Time is converted to numeric values (number of intervals since first observation)

References

[1] Hyndman, R.J., & Athanasopoulos, G. (2021). "Forecasting: principles and practice," 3rd edition, OTexts: Melbourne, Australia. OTexts.com/fpp3. Chapters 3.2 and 7.4.

Source Code

View on GitHub

Show/Hide source 
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
class PolynomialTrendForecaster(_BaseTrendForecaster):
    """Forecast using polynomial trend extrapolation with ElasticNet regularization.

    Fits a polynomial of specified degree to the historical data using ElasticNet
    regression and extrapolates into the future. Linear trend is the special case
    with degree=1.

    Parameters
    ----------
    degree : int, default=1
        Polynomial degree. degree=1 gives linear trend, degree=2 quadratic, etc.
        Higher degrees can overfit - typically use degree <= 3.
    estimator : RegressorMixin, default=ElasticNet()
        Regression model used to fit polynomial coefficients.
    target_transformer : BaseTransformer, optional
        Transformer for target variable (e.g., LogTransformer).
    panel_strategy : {"global", "multivariate"}, default="global"
        How to handle panel data.  See `BaseForecaster` for details.

    Attributes
    ----------
        Fitted sklearn Pipeline with a polynomial feature transformer and the provided
        a clone of the `estimator` model.

    Examples
    --------
    >>> import polars as pl
    >>> from datetime import datetime
    >>> from yohou.stationarity import PolynomialTrendForecaster
    >>>
    >>> # Create time series with linear trend
    >>> y = pl.DataFrame({
    ...     "time": pl.datetime_range(
    ...         start=datetime(2020, 1, 1), end=datetime(2020, 12, 31), interval="1d", eager=True
    ...     ),
    ...     "value": range(366),
    ... })
    >>>
    >>> # Fit linear trend forecaster
    >>> forecaster = PolynomialTrendForecaster(degree=1)
    >>> forecaster.fit(y, forecasting_horizon=7)
    PolynomialTrendForecaster()
    >>>
    >>> # Forecast next 7 days
    >>> y_pred = forecaster.predict(forecasting_horizon=7)

    See Also
    --------
    - [`PatternSeasonalityForecaster`][yohou.stationarity.seasonality.PatternSeasonalityForecaster] : Seasonal pattern extraction for periodic components.
    - [`FourierSeasonalityForecaster`][yohou.stationarity.seasonality.FourierSeasonalityForecaster] : Fourier-based seasonality estimation.
    - [`DecompositionPipeline`][yohou.compose.decomposition_pipeline.DecompositionPipeline] : Combines trend + seasonality + residual forecasters.

    Notes
    -----
    - For exponential trends, consider using target_transformer=LogTransformer()
      with degree=1
    - Polynomial trends can overfit - use with caution (typically degree <= 3)
    - Time is converted to numeric values (number of intervals since first observation)

    References
    ----------
    [1] Hyndman, R.J., & Athanasopoulos, G. (2021). "Forecasting:
        principles and practice," 3rd edition, OTexts: Melbourne, Australia.
        OTexts.com/fpp3. Chapters 3.2 and 7.4.

    """

    _parameter_constraints: dict = {
        "degree": [Interval(numbers.Integral, 0, None, closed="left")],
        "estimator": [RegressorMixin],
    }

    def __init__(
        self,
        degree: StrictInt = 1,
        estimator: RegressorMixin = ElasticNet(),
        target_transformer=None,
        panel_strategy="global",
    ):
        super().__init__(target_transformer=target_transformer, panel_strategy=panel_strategy)
        self.degree = degree
        self.estimator = estimator

    def _fit(
        self,
        y_t: pl.DataFrame | dict[str, pl.DataFrame],
        X_t: pl.DataFrame | dict[str, pl.DataFrame] | None,
        forecasting_horizon: StrictInt,
    ) -> None:
        """Fit polynomial trend model to transformed data.

        Parameters
        ----------
        y_t : pl.DataFrame or dict[str, pl.DataFrame]
            Transformed target time series.
        X_t : pl.DataFrame or dict[str, pl.DataFrame] or None
            Transformed features (unused).
        forecasting_horizon : int
            Number of steps ahead to forecast.

        """
        estimator = Pipeline([
            ("poly_features", PolynomialFeatures(degree=self.degree, include_bias=True)),
            ("regressor", clone(self.estimator)),
        ])

        self._fit_estimator(estimator, y_t)

Tutorials

The following example notebooks use this component:

  • Decomposition

    Data-Features

    Chain PolynomialTrendForecaster, PatternSeasonalityForecaster, and FourierSeasonalityForecaster inside DecompositionPipeline with component visualisation.

    View · Open in marimo

  • How to Build a Feature Pipeline

    Data-Features

    Nest FeaturePipeline, FeatureUnion, and DecompositionPipeline for multi-level feature engineering with trend-season-residual decomposition.

    View · Open in marimo

  • How to Choose a Decomposition Strategy

    Forecasting-Models

    Build 2- and 3-component DecompositionPipeline forecasters chaining trend, seasonality, and residual models with target pre-transformation.

    View · Open in marimo

  • How to Build Panel Feature Pipelines

    Panel-Data

    Combine ColumnForecaster, FeaturePipeline, FeatureUnion, and DecompositionPipeline on panel data with per-group scoring on KDD Cup air quality.

    View · Open in marimo

  • How to Apply Stationarity to Panel Data

    Panel-Data

    Apply per-group stationarity transforms on panel data with SeasonalDifferencing, DecompositionPipeline (polynomial trend + pattern seasonality), and residuals.

    View · Open in marimo

  • Quickstart

    Quickstart

    Comprehensive end-to-end tour of yohou beyond the Getting Started tutorials, covering data loading, baseline forecasting, preprocessing pipelines, decomposition, cross-validation search, and interval prediction.

    View · Open in marimo

  • Forecast Visualization

    Visualization

    Visualise point forecasts from single and multiple models, decomposition pipeline components, and time weight decay functions with interactive Plotly.

    View · Open in marimo