[Paper Review] Discovering contemporaneous and lagged causal relations in autocorrelated nonlinear time series datasets

Jakob Runge|arXiv (Cornell University)|Mar 7, 2020

Time Series Analysis and Forecasting65 citations

TL;DR

PCMCI+ is a conditional-independence based method that discovers both lagged and contemporaneous causal relations in autocorrelated nonlinear time series, with improved calibration, higher adjacency/orientation recall, and faster runtimes than PC.

ABSTRACT

The paper introduces a novel conditional independence (CI) based method for linear and nonlinear, lagged and contemporaneous causal discovery from observational time series in the causally sufficient case. Existing CI-based methods such as the PC algorithm and also common methods from other frameworks suffer from low recall and partially inflated false positives for strong autocorrelation which is an ubiquitous challenge in time series. The novel method, PCMCI$^+$, extends PCMCI [Runge et al., 2019b] to include discovery of contemporaneous links. PCMCI$^+$ improves the reliability of CI tests by optimizing the choice of conditioning sets and even benefits from autocorrelation. The method is order-independent and consistent in the oracle case. A broad range of numerical experiments demonstrates that PCMCI$^+$ has higher adjacency detection power and especially more contemporaneous orientation recall compared to other methods while better controlling false positives. Optimized conditioning sets also lead to much shorter runtimes than the PC algorithm. PCMCI$^+$ can be of considerable use in many real world application scenarios where often time resolutions are too coarse to resolve time delays and strong autocorrelation is present.

Motivation & Objective

• Develop a CI-based framework for causal discovery in time series that handles both lagged and contemporaneous links.
• Improve reliability of CI tests under strong autocorrelation by optimizing conditioning sets.
• Achieve higher adjacency detection and orientation recall with controlled false positives and faster runtimes.

Proposed method

• Introduce PCMCI+, an extension of PCMCI, to include contemporaneous link discovery.
• Separate edge removal into lagged and contemporaneous conditioning phases with fewer CI tests.
• Use momentary conditional independence (MCI) conditioning to calibrate tests under autocorrelation and boost effect sizes.
• Prove soundness (correct adjacencies) and, with Faithfulness, completeness (maximal orientation) of PCMCI+.
• Show order-independence and empirical gains in adjacency detection, orientation recall, and runtime over PC in simulations.

Experimental results

Research questions

• RQ1 Can a CI-based causal discovery method reliably identify both lagged and contemporaneous links in autocorrelated nonlinear time series?
• RQ2 Do optimized conditioning sets and MCI-based testing improve detection power and false positive control under autocorrelation?
• RQ3 Is PCMCI+ order-independent and computationally more efficient than existing approaches like PC while maintaining accuracy?
• RQ4 How does PCMCI+ perform across linear and nonlinear, Gaussian and non-Gaussian noise, and various levels of autocorrelation?
• RQ5 What theoretical guarantees (soundness/completeness) hold for PCMCI+ under standard causal assumptions?

Key findings

• PCMCI+ yields higher adjacency detection power and better contemporaneous orientation recall than PC under strong autocorrelation.
• PCMCI+ provides better false positive control and shorter runtimes compared to PC.
• Optimized conditioning sets and the MCI testing framework increase test effect sizes, improving detection power for contemporaneous links.
• PCMCI+ is sound and, with Faithfulness, complete, and order-independent in the causal graph reconstruction.
• The method is applicable flexibly to different CI tests and data types, including nonlinear and multivariate settings.