High-Dimensional Learning in Finance
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916825122471936 |
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| author | Fallahgoul, Hasan |
| author_facet | Fallahgoul, Hasan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_03780 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | High-Dimensional Learning in Finance Fallahgoul, Hasan Statistical Finance Machine Learning Econometrics 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. |
| title | High-Dimensional Learning in Finance |
| topic | Statistical Finance Machine Learning Econometrics |
| url | https://arxiv.org/abs/2506.03780 |