Juan Carlos Escanciano, Ricardo Parra
arXiv 20 Feb 2024 · Econometrics · publishedJournal of Business and Economic Statistics (2025) · 1 citations (OpenAlex)
arXiv:2402.12838 · PDF · DOI · OpenAlex · Extracted main text
The use of machine learning methods for predictive purposes has increased dramatically over the past two decades, but uncertainty quantification for predictive comparisons remains elusive. This paper addresses this gap by extending the classic inference theory for predictive ability in time series to modern machine learners, such as the Lasso or Deep Learning. We investigate under which conditions such extensions are possible. For standard out-of-sample asymptotic inference to be valid with machine learning, two key properties must hold: (I) a zero-mean condition for the score of the prediction loss function and (ii) a "fast rate" of convergence for the machine learner. Absent any of these conditions, the estimation risk may be unbounded, and inferences invalid and very sensitive to sample splitting. For accurate inferences, we recommend an 80%-20% training-test splitting rule. We illustrate the wide applicability of our results with three applications: high-dimensional time series regressions with the Lasso, Deep learning for binary outcomes, and a new out-of-sample test for the Martingale Difference Hypothesis (MDH). The theoretical results are supported by extensive Monte Carlo simulations and an empirical application evaluating the MDH of some major exchange rates at daily and higher frequencies.
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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 | West, K. D (1996) Asymptotic inference about predictive ability | 1.000 | 7 | 3 | 100% |
| 2 | Diebold, F. X. and R. Mariano (1995) Comparing predictive accuracy | 1.000 | 5 | 3 | 100% |
| 3 | Andrews, D. W (1994) Asymptotics for semiparametric econometric models via stochastic equicontinuity | 0.843 | 3 | 3 | 100% |
| 4 | Gneiting, T (2011) Making and evaluating point forecasts | 0.737 | 3 | 2 | 100% |
| 5 | Kengne, W. and M. Wade (2024) Deep learning from strongly mixing observations: Sparse-penalized regularization and minimax optimality | 0.737 | 3 | 2 | 100% |
| 6 | Wong, K. C., Z. Li, and A. Tewari (2020) Lasso guarantees for $ $-mixing heavy-tailed time series | 0.737 | 3 | 2 | 100% |
| 7 | Clark, T. E. and K. D. West (2006) Using out-of-sample mean squared prediction errors to test the martingale difference hypothesis | 0.693 | 6 | 1 | 100% |
| 8 | Escanciano, J. C. and I. N. Lobato (2009) An automatic portmanteau test for serial correlation self | 0.644 | 4 | 1 | 100% |
| 9 | Escanciano, J. C. and I. N. Lobato (2009) Testing the martingale hypothesis self | 0.511 | 2 | 1 | 100% |
| 10 | Greenshtein, E. and Y. Ritov (2004) Persistence in high-dimensional linear predictor selection and the virtue of overparametrization | 0.511 | 2 | 1 | 100% |
Showing the top 10 of 28 scored citations.