Year: 2025
Type: article
Abstract: Penalized estimation methods for diffusion processes and dependent data have recently gained significant attention due to their effectiveness in handling stochastic systems. In this work, we introduce an adaptive Elastic-Net estimator for ergodic diffusion processes observed under high-frequency sampling schemes. Our method combines the least squares approximation of the quasi-likelihood with adaptive $$\ell _1$$ ℓ 1 and $$\ell _2$$ ℓ 2 regularization. This approach allows to enhance prediction accuracy and interpretability while effectively recovering the sparse underlying structure of the model. In the spirit of recent research trends, we provide finite-sample guarantees for the (block-diagonal) estimator’s performance by deriving high-probability non-asymptotic bounds for the $$\ell _2$$ ℓ 2 estimation error. These results complement the established oracle properties in the high-frequency asymptotic regime with mixed convergence rates, ensuring consistent selection of the relevant interactions and achieving optimal rates of convergence. Furthermore, we utilize our results to analyze one-step-ahead predictions, offering non-asymptotic control over the $$\ell _1$$ ℓ 1 prediction error. The performance of our method is evaluated through simulations and real data applications, demonstrating its effectiveness, particularly in scenarios with strongly correlated variables.
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
Funder: Sapienza Università di Roma
OpenAlex ID: W4417280449