Forecasting the monthly retail sales of electricity based on the semi-functional linear model with autoregressive errors

Bin Yang; Min Chen; Jianjun Zhou; Bin Yang; Min Chen; Jianjun Zhou

doi:10.3934/math.2025074

AIMS Mathematics

2025, Volume 10, Issue 1: 1602-1627. doi: 10.3934/math.2025074

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Research article

Forecasting the monthly retail sales of electricity based on the semi-functional linear model with autoregressive errors

1.
Yunnan Key Laboratory of Statistical Modeling and Data Analysis, Yunnan University, Kunming 650091, China
2.
City College, Kunming University of Science and Technology, Kunming 650051, China
3.
School of Mathematical Sciences, Shanxi University, Taiyuan 030006, China
4.
Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

Received: 03 October 2024 Revised: 04 January 2025 Accepted: 14 January 2025 Published: 23 January 2025
MSC : 62J05, 62P12

In many statistical applications, data are collected sequentially over time and exhibit autocorrelation characteristics. Ignoring this autocorrelation may lead to a decrease in the model's prediction accuracy. To this end, assuming that the error process is an autoregressive process, this paper introduced a semi-functional linear model with autoregressive errors. Based on the functional principal component analysis and the spline method, we obtained the estimators of the slope function, nonparametric function, and autoregressive coefficients. Under some regular conditions, we found the convergence rate of the proposed estimators. A simulation study was conducted to investigate the finite sample performance of the proposed estimators. Finally, we applied our model to forecast the monthly retail sales of electricity, which illustrates the validity of our model from a predictive perspective.
- semi-functional linear model,
- autoregressive errors,
- convergence rate,
- functional principal component analysis,
- spline estimation
Citation: Bin Yang, Min Chen, Jianjun Zhou. Forecasting the monthly retail sales of electricity based on the semi-functional linear model with autoregressive errors[J]. AIMS Mathematics, 2025, 10(1): 1602-1627. doi: 10.3934/math.2025074

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Abstract

In many statistical applications, data are collected sequentially over time and exhibit autocorrelation characteristics. Ignoring this autocorrelation may lead to a decrease in the model's prediction accuracy. To this end, assuming that the error process is an autoregressive process, this paper introduced a semi-functional linear model with autoregressive errors. Based on the functional principal component analysis and the spline method, we obtained the estimators of the slope function, nonparametric function, and autoregressive coefficients. Under some regular conditions, we found the convergence rate of the proposed estimators. A simulation study was conducted to investigate the finite sample performance of the proposed estimators. Finally, we applied our model to forecast the monthly retail sales of electricity, which illustrates the validity of our model from a predictive perspective.

References

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