Sven Otto, Luis Winter
arXiv 16 Mar 2025 · Econometrics
arXiv:2503.12611 · PDF · Extracted main text
We propose a function-on-function linear regression model for time-dependent curve data that is consistently estimated by imposing factor structures on the regressors. An integral operator based on cross-covariances identifies two components for each functional regressor: a predictive low-dimensional component, along with associated factors that are guaranteed to be correlated with the dependent variable, and an infinite-dimensional component that has no predictive power. In order to consistently estimate the correct number of factors for each regressor, we introduce a functional eigenvalue difference test. While conventional estimators for functional linear models fail to converge in distribution, we establish asymptotic normality, making it possible to construct confidence bands and conduct statistical inference. The model is applied to forecast electricity price curves in three different energy markets. Its prediction accuracy is found to be comparable to popular machine learning approaches, while providing statistically valid inference and interpretable insights into the conditional correlation structures of electricity prices.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Otto, Sven, Salish, Nazarii (2025) Approximate Factor Models for Functional Time Series self | 0.928 | 4 | 3 | 100% |
| 2 | Benatia, David, Carrasco, Marine, Florens, Jean-Pierre (2017) Functional linear regression with functional response | 0.737 | 3 | 2 | 100% |
| 3 | Crambes, Christophe, Mas, André (2013) Asymptotics of prediction in functional linear regression with functional outputs | 0.737 | 3 | 2 | 100% |
| 4 | Hörmann, Siegfried, Jammoul, Fatima (2023) Prediction in functional regression with discretely observed and noisy covariates | 0.737 | 3 | 2 | 100% |
| 5 | Mas, André (2007) Weak convergence in the functional autoregressive model | 0.737 | 3 | 2 | 100% |
| 6 | Wu, Jianhong (2018) Eigenvalue difference test for the number of common factors in the approximate factor models | 0.737 | 3 | 2 | 100% |
| 7 | Lago, Jesus, Marcjasz, Grzegorz, Schutter, Bart (2021) Forecasting day-ahead electricity prices: A review of state-of-the-art algorithms, best practices and an open-access benchmark | 0.693 | 5 | 1 | 100% |
| 8 | Imaizumi, Masaaki, Kato, Kengo (2018) PCA-based estimation for functional linear regression with functional responses | 0.644 | 2 | 2 | 100% |
| 9 | Liebl, Dominik (2013) Modeling and forecasting electricity spot prices: A functional data perspective | 0.644 | 2 | 2 | 100% |
| 10 | White, Halbert (2001) Asymptotic theory for econometricians | 0.511 | 5 | 2 | 20% |
Showing the top 10 of 47 scored citations.