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High resolution temperature forecasting using functional time series decomposition and advanced predictive models.

Huda M Alshanbari¹, Musaad S Aldhabani², Naveed Iqbal³

¹Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O.Box 84428, Riyadh, 11671, Saudi Arabia.

Scientific Reports

|February 25, 2026

Summary

This summary is machine-generated.

Accurate air temperature (AT) forecasting is crucial. A functional autoregressive model (FAR(1)) using functional time series analysis demonstrates superior prediction accuracy and stability over traditional and machine learning methods.

Keywords:

ARIMA Functional autoregressive Functional data analysis Vector autoregressive

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Area of Science:

Environmental Science
Data Science
Statistical Modeling

Background:

Air temperature (AT) significantly impacts environmental processes, human health, agriculture, and energy systems.
Accurate forecasting of AT is essential for informed decision-making in various sectors.
High-frequency temperature data exhibits smooth, periodic dynamics influenced by seasonal cycles and stochastic factors.

Purpose of the Study:

To explore the prediction of air temperature using a functional time series (FTS) model.
To model high-frequency temperature data as smooth daily curves, capturing both seasonal cycles and stochastic dynamics.
To evaluate the performance of the functional autoregressive model (FAR(1)) against classical statistical and machine learning models.

Main Methods:

Utilized smoothing splines and Fourier-based functional representations for modeling temperature data.
Employed a functional autoregressive model of order 1 (FAR(1)) for short-term AT variation prediction.
Compared FAR(1) performance against ARIMA, VAR, artificial neural networks (ANN), and autoregressive neural networks (ARNN) using MAE, MAPE, and RMSE metrics.

Main Results:

The FAR(1) model consistently achieved lower forecasting errors (MAE, MAPE, RMSE) compared to all benchmark models.
FAR(1) demonstrated enhanced predictive stability across both monthly and hourly forecasting horizons.
Functional data analysis proved effective in leveraging the inherent smooth and periodic structure of temperature data.

Conclusions:

The FAR(1) model offers a practical and holistic approach for predicting high-frequency air temperature.
Functional time series analysis is a valuable tool for environmental data prediction, outperforming traditional methods.
The findings support the application of this model for improved decision-making in agriculture, energy management, and safety during climate variability.