arXiv 4 Jun 2025 · Finance — Statistical Finance · 3 citations (OpenAlex)
arXiv:2506.03780 · PDF · DOI · OpenAlex · Extracted main text
Recent advances in machine learning have shown promising results for financial prediction using large, over-parameterized models. This paper provides theoretical foundations and empirical validation for understanding when and how these methods achieve predictive success. I examine two key aspects of high-dimensional learning in finance. First, I prove that within-sample standardization in Random Fourier Features implementations fundamentally alters the underlying Gaussian kernel approximation, replacing shift-invariant kernels with training-set dependent alternatives. Second, I establish information-theoretic lower bounds that identify when reliable learning is impossible no matter how sophisticated the estimator. A detailed quantitative calibration of the polynomial lower bound shows that with typical parameter choices, e.g., 12,000 features, 12 monthly observations, and R-square 2-3%, the required sample size to escape the bound exceeds 25-30 years of data--well beyond any rolling-window actually used. Thus, observed out-of-sample success must originate from lower-complexity artefacts rather than from the intended high-dimensional mechanism.
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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 | Rahimi \ Recht (2007) Random features for large-scale kernel machines, in `Advances in Neural Information Processing Systems', Vol. 20, pp. 1177–1184 | 1.000 | 11 | 6 | 100% |
| 2 | Nagel (2025) `Seemingly virtuous complexity in return prediction', Working paper | 1.000 | 7 | 3 | 100% |
| 3 | Kelly, Malamud \ Zhou (2024) `The virtue of complexity in return prediction', Journal of Finance 79(1), 459–503 | 0.981 | 18 | 7 | 94% |
| 4 | Welch \ Goyal (2008) `A comprehensive look at the empirical performance of equity premium prediction', Review of Financial Studies 21(4), 1455–1508 | 0.811 | 4 | 2 | 100% |
| 5 | Gu, Kelly \ Xiu (2020) `Empirical asset pricing via machine learning', Review of Financial Studies 33(5), 2223–2273 | 0.737 | 3 | 2 | 100% |
| 6 | Sutherland \ Schneider (2015) On the error of random fourier features, in `Proceedings of the Thirty-First Conference on Uncertainty in Artificial Intelligenc… | 0.644 | 2 | 2 | 100% |
| 7 | Vapnik (1998) Statistical Learning Theory, Wiley, New York | 0.511 | 3 | 2 | 33% |
| 8 | Shalev-Shwartz \ Ben-David (2014) Understanding Machine Learning: From Theory to Algorithms, Cambridge University Press, Cambridge, UK | 0.511 | 2 | 2 | 50% |
| 9 | Bianchi, Büchner \ Tamoni (2021) `Bond risk premiums with machine learning', Review of Financial Studies 34(2), 1046–1089 | 0.511 | 2 | 1 | 100% |
| 10 | Chen, Pelger \ Zhu (2024) `Deep learning in asset pricing', Management Science 70(2), 714–750 | 0.511 | 2 | 1 | 100% |
Showing the top 10 of 29 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Overparametrized models with posterior drift | 0.511 | 2 | 1 |