PolynomialTrendForecaster - degree parameter not working properly #8684

SueP12 · 2025-08-11T16:55:44Z

SueP12
Aug 11, 2025

Hello,

I noticed that the PolynomialTrendForecaster is not working as expected.
I made a comparison with an equivalent scikit-learn implementation, where they should produce the same results for the same degree setting.

However, in the example below, degrees 2, 3, and 4 all produce the same results as degree 2.
In my actual dataset, this behavior even starts from degree 1.

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from sklearn.pipeline import make_pipeline
from sklearn.preprocessing import PolynomialFeatures
from sklearn.linear_model import LinearRegression
from sktime.forecasting.trend import PolynomialTrendForecaster
from sktime.forecasting.base import ForecastingHorizon

def create_data():
    """
    Create synthetic time series data with cubic trend: up fast, then down, then up again.
    """
    dates = pd.date_range('2019-01-01', '2024-12-31', freq='D')
    n = len(dates)
    t = np.linspace(-1, 1, n)
    trend = 1000 + 500 * t + 200 * t**2 - 300 * t**3
    noise = np.random.normal(0, 20, n)
    y = trend + noise
    df = pd.DataFrame({
        'DATE': dates,
        'VALUE': y
    })
    
    return df

def plot_polynomial_trend_comparison(
    df: pd.DataFrame,
    target_col: str = "VALUE",
    date_col: str = "DATE", 
    max_degree: int = 3,
):
   
    # Prepare data
    df = df.copy()
    df = df.set_index(date_col)
    df = df.sort_index()
    df["time_int"] = np.arange(len(df))
    
    # Convert to pandas Series for sktime
    y_series = df[target_col]

    # Create subplots: rows for degrees, columns for sklearn vs sktime
    n_plots = max_degree + 1
    fig, axs = plt.subplots(n_plots, 2, figsize=(20, 5 * n_plots), sharex=True)
    
    for degree in range(n_plots):
        ax_sklearn = axs[degree, 0]
        ax_sklearn.scatter(df.index, df[target_col], color="lightgray", s=5, alpha=0.6, label="Full data")
        ax_sktime = axs[degree, 1]
        ax_sktime.scatter(df.index, df[target_col], color="lightgray", s=5, alpha=0.6, label="Full data")
        
        # sklearn
        pipe = make_pipeline(
            PolynomialFeatures(degree=degree, include_bias=True),
            LinearRegression(fit_intercept=False),
        )
        pipe.fit(df["time_int"].values.reshape(-1, 1), df[target_col].values)
        y_trend_sklearn = pipe.predict(df["time_int"].values.reshape(-1, 1))

        ax_sklearn.plot(
            df.index,
            y_trend_sklearn,
            color="red",
            linestyle="-",
            linewidth=3,
            label="Sklearn trend",
            alpha=0.85,
        )
        
        # sktime
        trend_forecaster = PolynomialTrendForecaster(degree=degree)
        trend_forecaster.fit(y_series)
        
        fh = ForecastingHorizon(df.index)
        y_trend_sktime = trend_forecaster.predict(fh)
        
        ax_sktime.plot(
            df.index,
            y_trend_sktime,
            color="blue",
            linestyle="-",
            linewidth=3,
            label="Sktime trend",
            alpha=0.85,
        )
        
        # Set titles and labels
        ax_sklearn.set_title(f"Sklearn - Polynomial Degree {degree}")
        ax_sktime.set_title(f"Sktime - Polynomial Degree {degree}")
        
        ax_sklearn.set_ylabel(target_col)
        ax_sktime.set_ylabel(target_col)
        
        ax_sklearn.legend(loc="upper left", fontsize=10)
        ax_sktime.legend(loc="upper left", fontsize=10)
        
    axs[-1, 0].set_xlabel("Date")
    axs[-1, 1].set_xlabel("Date")
    
    plt.tight_layout()
    plt.show()


df = create_data()
plot_polynomial_trend_comparison(df, max_degree=4)

Has anyone experienced this before or knows where this behavior might be coming from?

fkiraly · 2025-08-11T18:17:14Z

fkiraly
Aug 11, 2025
Maintainer

This is very strange - what is inside is exactly the scikit-learn pipeline, just with a bit of syntactic sugar around it to make it sktime compatible. It is strange that you see this behaviour.

May I request that you report what you get if you print trend_forecaster.regressor_ and trend_forecaster.regressor_.get_params(), at the end of each loop?

As well as your sktime show_versions output?

1 reply

SueP12 Aug 11, 2025
Author

Thank you for your fast reply. Here is the output:

regressor_:
Pipeline(steps=[('polynomialfeatures', PolynomialFeatures(degree=0)),
('linearregression', LinearRegression(fit_intercept=False))])
regressor_.get_params():
memory: None
steps: [('polynomialfeatures', PolynomialFeatures(degree=0)), ('linearregression', LinearRegression(fit_intercept=False))]
transform_input: None
verbose: False
polynomialfeatures: PolynomialFeatures(degree=0)
linearregression: LinearRegression(fit_intercept=False)
polynomialfeatures__degree: 0
polynomialfeatures__include_bias: True
polynomialfeatures__interaction_only: False
polynomialfeatures__order: C
linearregression__copy_X: True
linearregression__fit_intercept: False
linearregression__n_jobs: None
linearregression__positive: False
linearregression__tol: 1e-06
regressor_:
Pipeline(steps=[('polynomialfeatures', PolynomialFeatures(degree=1)),
('linearregression', LinearRegression(fit_intercept=False))])
regressor_.get_params():
memory: None
steps: [('polynomialfeatures', PolynomialFeatures(degree=1)), ('linearregression', LinearRegression(fit_intercept=False))]
transform_input: None
verbose: False
polynomialfeatures: PolynomialFeatures(degree=1)
linearregression: LinearRegression(fit_intercept=False)
polynomialfeatures__degree: 1
polynomialfeatures__include_bias: True
polynomialfeatures__interaction_only: False
polynomialfeatures__order: C
linearregression__copy_X: True
linearregression__fit_intercept: False
linearregression__n_jobs: None
linearregression__positive: False
linearregression__tol: 1e-06
regressor_:
Pipeline(steps=[('polynomialfeatures', PolynomialFeatures()),
('linearregression', LinearRegression(fit_intercept=False))])
regressor_.get_params():
memory: None
steps: [('polynomialfeatures', PolynomialFeatures()), ('linearregression', LinearRegression(fit_intercept=False))]
transform_input: None
verbose: False
polynomialfeatures: PolynomialFeatures()
linearregression: LinearRegression(fit_intercept=False)
polynomialfeatures__degree: 2
polynomialfeatures__include_bias: True
polynomialfeatures__interaction_only: False
polynomialfeatures__order: C
linearregression__copy_X: True
linearregression__fit_intercept: False
linearregression__n_jobs: None
linearregression__positive: False
linearregression__tol: 1e-06
regressor_:
Pipeline(steps=[('polynomialfeatures', PolynomialFeatures(degree=3)),
('linearregression', LinearRegression(fit_intercept=False))])
regressor_.get_params():
memory: None
steps: [('polynomialfeatures', PolynomialFeatures(degree=3)), ('linearregression', LinearRegression(fit_intercept=False))]
transform_input: None
verbose: False
polynomialfeatures: PolynomialFeatures(degree=3)
linearregression: LinearRegression(fit_intercept=False)
polynomialfeatures__degree: 3
polynomialfeatures__include_bias: True
polynomialfeatures__interaction_only: False
polynomialfeatures__order: C
linearregression__copy_X: True
linearregression__fit_intercept: False
linearregression__n_jobs: None
linearregression__positive: False
linearregression__tol: 1e-06
regressor_:
Pipeline(steps=[('polynomialfeatures', PolynomialFeatures(degree=4)),
('linearregression', LinearRegression(fit_intercept=False))])
regressor_.get_params():
memory: None
steps: [('polynomialfeatures', PolynomialFeatures(degree=4)), ('linearregression', LinearRegression(fit_intercept=False))]
transform_input: None
verbose: False
polynomialfeatures: PolynomialFeatures(degree=4)
linearregression: LinearRegression(fit_intercept=False)
polynomialfeatures__degree: 4
polynomialfeatures__include_bias: True
polynomialfeatures__interaction_only: False
polynomialfeatures__order: C
linearregression__copy_X: True
linearregression__fit_intercept: False
linearregression__n_jobs: None
linearregression__positive: False
linearregression__tol: 1e-06

System:
python: 3.10.16 (main, Jun 25 2025, 17:40:50) [Clang 17.0.0 (clang-1700.0.13.5)]
machine: macOS-15.6-arm64-arm-64bit

Python dependencies:
pip: 25.1.1
sktime: 0.38.4
sklearn: 1.7.0
skbase: 0.12.3
numpy: 1.26.4
scipy: 1.15.3
pandas: 2.3.0
matplotlib: 3.10.3
joblib: 1.5.1
numba: 0.61.2
statsmodels: 0.14.4
pmdarima: 2.0.4
statsforecast: 2.0.1
tsfresh: None
tslearn: None
torch: None
tensorflow: None

fkiraly · 2025-08-11T18:30:32Z

fkiraly
Aug 11, 2025
Maintainer

I can reproduce the plots, this is clearly a bug that needs to be investigated - could you please open a bug report?

copy over your code
and the show_versions output

Here is my printout for regressor_:

Pipeline(steps=[('polynomialfeatures', PolynomialFeatures(degree=0)),
                ('linearregression', LinearRegression(fit_intercept=False))])
Pipeline(steps=[('polynomialfeatures', PolynomialFeatures(degree=1)),
                ('linearregression', LinearRegression(fit_intercept=False))])
Pipeline(steps=[('polynomialfeatures', PolynomialFeatures()),
                ('linearregression', LinearRegression(fit_intercept=False))])
Pipeline(steps=[('polynomialfeatures', PolynomialFeatures(degree=3)),
                ('linearregression', LinearRegression(fit_intercept=False))])
Pipeline(steps=[('polynomialfeatures', PolynomialFeatures(degree=4)),
                ('linearregression', LinearRegression(fit_intercept=False))])

The mystery grows...

1 reply

SueP12 Aug 11, 2025
Author

I opened a bug report here: #8686

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PolynomialTrendForecaster - degree parameter not working properly #8684

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fkiraly Aug 11, 2025 Maintainer

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fkiraly
Aug 11, 2025
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fkiraly
Aug 11, 2025
Maintainer

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