Cross-validation for nonstationary financial time series and hyperparameter selection

Develop cross-validation procedures that appropriately estimate both model parameters and hyperparameters for regularized high-dimensional realized variance forecasting models under nonstationary financial time series, ensuring that temporal ordering and structural changes are respected.

Background

Regularized models such as LASSO require hyperparameter selection, commonly via K-fold cross-validation. In nonstationary financial data, the temporal position of validation folds relative to training folds can affect performance because time direction matters. The authors state that conventional cross-validation may be unsuitable and identify the need for methods tailored to nonstationary settings.

References

When data is nonstationary, it isn't clear that K-fold cross-validation is the best methodology for estimating parameters, because the direction of time can matter. So far, there has been little research in tackling this question and is an important open question, which we leave for future work.

— Predicting Realized Variance Out of Sample: Can Anything Beat The Benchmark?  (2506.07928 - Pollok, 9 Jun 2025) in Section 4.2, High-Dimensional Regularized Models of Realized Variance

Refit-after-selection, and the slice's size and position (fixed at the adjacent 20\% throughout), remain unexplored.

— When Does Online Adaptation Pay on the Edge? A Leakage-Free Evaluation of Warmup, Learning-Rate Selection, and Resource Trade-offs for Time-Series Forecasting  (2609.01126 - Fujimoto et al., 1 Sep 2026) in Discussion and Limitations, Section 5