# Causal Lag Structure Discovery in Confounded Time Series via Orthogonalized Adaptive Estimation

arXiv: https://arxiv.org/abs/2610.05618 · HTML: https://mlsanity.com/paper/2610.05618/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 42 references that are in the map.
- First posted on arXiv 4 Oct 2026.

## Builds on (most cited first, 11 of 11)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Detecting causal associations in large nonlinear time series datasets](https://mlsanity.com/paper/1702.07007/) (2017)
- [DYNOTEARS: Structure Learning from Time-Series Data](https://mlsanity.com/paper/2002.00498/) (2020)
- [Regularized estimation in sparse high-dimensional time series models](https://mlsanity.com/paper/1311.4175/) (2013)
- [Double Machine Learning Based Structure Identification from Temporal Data](https://mlsanity.com/paper/2311.06012/) (2023)
- [Granger Causality Testing in High-Dimensional VARs: a Post-Double-Selection Procedure](https://mlsanity.com/paper/1902.10991/) (2019)
- [Semiparametric inference for impulse response functions using double/debiased machine learning](https://mlsanity.com/paper/2411.10009/) (2024)
- [Discovering the Network Granger Causality in Large Vector Autoregressive Models](https://mlsanity.com/paper/2303.15158/) (2023)
- [The dynamic generalized covariance measure for conditional independence testing with nonstationary time series](https://mlsanity.com/paper/2504.21647/) (2025)
- [Conditional Independence Testing in Time Series](https://mlsanity.com/paper/2609.20772/) (2026)
- [Semiparametric Inference for Dynamic Causal Effects from Observational Time Series](https://mlsanity.com/paper/2609.27531/) (2026)

## Abstract (arXiv)

Finding which variables cause which others in multivariate time series, and at what lags, is central to science and policy, yet existing methods force a choice between flexible confounder adjustment, data-driven lag selection, and inference that controls the false discovery rate (FDR). ORACLE-VARX does all three in one pipeline. First, double/debiased machine learning (DML) removes nonlinear confounder effects from the outcomes and the lagged series. Second, adaptive causal lag estimation (ACLE) picks the lag order at each time step by sequential significance tests, tracking regime changes. Third, entry-wise z-tests with Benjamini--Hochberg correction select directed edges at a target FDR. We prove that in each rolling window, the debiased coefficients are asymptotically normal around a window-averaged target, so their z-tests are asymptotically valid. On a synthetic benchmark with time-varying structure and nonlinear confounding, ORACLE-VARX (LightGBM) tracks the true lag order best (RMSE 0.96 vs 1.1--1.5), has edge FDR 0.047, close to PCMCI (0.045) and below VAR (0.129) and VAR-LiNGAM (0.187), and forecasts better than all three. On nine U.S. sector ETFs with macroeconomic confounders, it yields interpretable causal graphs whose lag order rises in high-volatility regimes.