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Should Model Complexity and Training Windows Be Chosen Together?

Bottom line: More historical data can stabilize a complex model while importing obsolete relationships. ATOMS jointly addresses candidate-model and window selection, with reported gains for U.S. industry returns. Its assumptions, information timing, unusual Sharpe definition and light cost parameter limit any direct deployment interpretation.

Source and version

  • Agostino Capponi, Chengpiao Huang, J. Antonio Sidaoui, Kaizheng Wang and Jiacheng Zou
  • The Nonstationarity-Complexity Tradeoff in Return Prediction
  • Official SSRN record · DOI
  • First posted: December 29, 2025; last revised: August 13, 2026
  • Reviewed: the 109-page August 13, 2026 PDF, including appendices A–G. No independent replication or step-by-step certification of all proofs
  • Filed under 2025 Q4 by SSRN posting. This current reading of the 2026 revision is not a point-in-time snapshot of the 2025 text
  • Preprint. The authors link ATOMS code; we did not run or audit it

The tradeoff

Under stated assumptions, the authors decompose squared-error excess-risk bounds into approximation, estimation and distribution-shift terms. Complexity can reduce misspecification but require more samples; a longer history reduces estimation noise but may mix obsolete regimes. This does not imply that either simpler models or shorter windows always win.

Two windows matter:

  • The training window determines which observations fit a candidate.
  • The validation lookback determines which historical losses compare fitted candidates.

ATOMS builds candidates across model classes, hyperparameters and training windows. It selects a validation lookback for each pair using loss differences, then applies a randomized elimination tournament. Expected linear comparison count excludes the cost of training the candidate grid.

Data and reported results

The study covers 17 U.S. industries and 129 predictors, September 1987–November 2016, with OOS evaluation from January 1990. Daily models use macro/SDF factors, Fama–French factors, characteristic-sorted portfolios and lagged industry returns. Candidates include RF, Ridge, LASSO and Elastic Net.

Past months are split 80/20 for training and validation, repeated over 20 seeds, before future-month evaluation. These are repeated algorithmic splits, not independent market histories or a ready-made design for overlapping labels.

Table 3 reports zero-forecast OOS \(R^2\) of 0.049 versus 0.043 for the strongest fixed-window benchmark: +0.006, or 0.6 percentage points, approximately 14% relatively. The financial-crisis comparison is narrower, 0.041 versus 0.039. Paper-defined stress windows should not be assumed identical to official recession dates.

These source-reported results were not replicated and do not establish performance for options or other prediction targets.

Important limits

Conditional theory

Theorems assume independent batches and bounded outcomes/predictions, with a balanced split for the joint-selection result. Conditional latent-state arguments do not establish validity under arbitrary dependence. The practical \(M'\) is calibrated to a pre-OOS percentile rather than an absolute bound; the authors' halving/doubling check does not automatically recover the exact theoretical confidence guarantee.

Nonstandard Sharpe aggregation

“Monthly Sharpe” is calculated from daily net-return mean/SD within each month, then averaged across months. Table 4 gives 0.333 versus 0.303 on that basis. These are not conventional full-sample monthly-return or annualized Sharpe ratios.

Light cost coefficient

The reported net-return rule is

\[ r_s=r_s^g-c\lVert w_s-w_{s-1}\rVert_1, \qquad c=\frac{4\times10^{-4}}{252}. \]

This is not 4 bp per unit turnover. It is not a full test of realistic spreads, impact, financing, capacity or execution delay, particularly for options.

Unaudited information timing

The appendix repeats monthly variables across days within a month and describes a size filter tied to month-end equity. Feature lags, releases, real-time vintages and generated macro/SDF inputs still need code-level checking. We have neither confirmed leakage nor established PIT safety. Chronological model evaluation alone cannot certify feature availability.

Research implications

  1. Evaluate model/window pairs against fixed-window, expanding-window and simple-model baselines on the same future period.
  2. Preserve paired validation losses. Overlapping labels still require suitable purging, embargo or dependence-aware inference.
  3. Match selection loss to the task. Conditional-mean MSE theory does not automatically cover quantile, interval-score, ranking or execution-utility objectives.
  4. Test on the actual information set before considering deployment; no production or trading changes follow from this reading.

Research boundary

Full-text reading is not independent proof certification, data replication or evidence of live-trading feasibility.