Double Machine Learning for Time Series

Double Machine Learning for Time Series

Milos Ciganovic
Federico D'Amario
Massimiliano Tancioni
Published on 3/11/2026
Cross-asset
Machine learning
Risk management

This paper adapts the Double Machine Learning (DML) estimator for macroeconomic time series, which are typically short, persistent, and highly endogenous. The key innovation is Reverse Cross-Fitting (RCF), a deterministic cross-fitting scheme that leverages the time-reversibility of stationary processes. Unlike random cross-fitting, RCF preserves the temporal structure by training nuisance functions on either past or time-reversed future data, avoiding the sample loss of block-based methods like Neighbors-Left-Out (NLO). The authors prove that under conditions of weak dependence, Neyman orthogonality, and conditional stability, the RCF-DML estimator is root-T consistent and asymptotically normal, with a long-run variance that can be consistently estimated via HAC methods.

A second contribution addresses hyperparameter tuning for nuisance learners. Standard predictive tuning (e.g., minimizing RMSE) can lead to high bias in high-dimensional settings, as it does not align with the bias-variance trade-off required for valid causal inference. The paper proposes a stability-based criterion that identifies a 'Goldilocks zone' of tuning parameters where the fold-specific RMSE varies minimally. Within this zone, the estimator achieves minimal bias, even when predictive RMSE is not minimized. Extensive simulations based on structural VAR and partially linear regression DGPs show that RCF-DML performs well in finite samples, outperforming NLO under strong persistence and remaining robust to model misspecification, heteroskedasticity, and non-normality. An empirical application to the dynamic effects of Tier 1 regulatory capital shocks demonstrates the method's practical utility, yielding results consistent with prior literature.

Highlights

  • 1Proposes Reverse Cross-Fitting (RCF) for time series, exploiting time-reversibility to improve sample usage and efficiency.
  • 2Establishes asymptotic normality and consistency of the RCF-DML estimator under weak dependence and conditional stability.
  • 3Introduces a stability-based tuning criterion (Goldilocks zone) that minimizes bias in high-dimensional settings, unlike predictive tuning.
  • 4Demonstrates robustness to model misspecification, heteroskedasticity, and non-normality through extensive simulations.
  • 5Applies the method to residualized Local Projections for estimating dynamic effects of regulatory capital shocks.

Methods

  • M
    Reverse Cross-Fitting (RCF): a deterministic cross-fitting scheme that uses time-reversed future or past data as auxiliary samples.
  • M
    Double/Debiased Machine Learning (DML) with Neyman orthogonal score and residual-on-residual OLS.
  • M
    Stability-based tuning: selects hyperparameters by minimizing a combined score of local RMSE variability and predictive error within a moving window.
  • M
    HAC variance estimation for long-run variance under serial dependence.

Results

  • R
    RCF-DML achieves root-T consistency and asymptotic normality with variance equal to the oracle long-run variance.
  • R
    In finite samples, RCF outperforms Neighbors-Left-Out (NLO) cross-fitting, especially under strong persistence.
  • R
    Stability-based tuning (Goldilocks zone) yields lower bias than predictive tuning in high-dimensional regimes.
  • R
    The estimator remains valid under model misspecification (e.g., ignoring recursivity) and non-Gaussian errors (GARCH).
  • R
    Empirical application to Tier 1 capital shocks produces impulse responses consistent with established identification strategies.
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