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<p>Granger causality analysis (GCA) via vector autoregression with regularization penalty identifies sparse causality in high-dimensional time series. However, the assumptions of linear relationship and uniform lag orders across variables and sensitivity to regularization parameter selection compromise causal discovery accuracy. To address these limitations, a quantile-adaptive distributional Granger causal model (QA-DGCM) is developed to infer non-causal paths via an <i>m</i>-stage hypothesis testings based on distributional Granger causal effect (DGCE) statistic. QA-DGCM treats variables’ quantiles as historical conditionings and quantifies non-linear causality by DGCE. To control the false discovery rate in hypothesis testing, an adaptive threshold is estimated based on the survival functions following asymptotic chi-square distributions to detect different causal relationships with high probability. Theoretical analysis establishes QA-DGCM’s asymptotic properties, including sure screening property and consistency, under mild conditions. As a model-free framework, QA-DGCM requires no specified distributional assumptions and adapts to diverse causality. Simulations demonstrate QA-DGCM’s superior accuracy over existing Granger methods across diverse causal structures. Applied to real-world time series data, it yields unique neurobiological insights advancing whole-brain effective connectivity analysis.</p>

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Quantile-adaptive distributional Granger causal model for high-dimensional time series

  • 期刊论文

  • 发表日期：

    2026年7月23日

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  • Zihao Yuan,
  • Jiaqing Chen,
  • Han Qiu,
  • Yangxin Huang

摘要

Granger causality analysis (GCA) via vector autoregression with regularization penalty identifies sparse causality in high-dimensional time series. However, the assumptions of linear relationship and uniform lag orders across variables and sensitivity to regularization parameter selection compromise causal discovery accuracy. To address these limitations, a quantile-adaptive distributional Granger causal model (QA-DGCM) is developed to infer non-causal paths via an m-stage hypothesis testings based on distributional Granger causal effect (DGCE) statistic. QA-DGCM treats variables’ quantiles as historical conditionings and quantifies non-linear causality by DGCE. To control the false discovery rate in hypothesis testing, an adaptive threshold is estimated based on the survival functions following asymptotic chi-square distributions to detect different causal relationships with high probability. Theoretical analysis establishes QA-DGCM’s asymptotic properties, including sure screening property and consistency, under mild conditions. As a model-free framework, QA-DGCM requires no specified distributional assumptions and adapts to diverse causality. Simulations demonstrate QA-DGCM’s superior accuracy over existing Granger methods across diverse causal structures. Applied to real-world time series data, it yields unique neurobiological insights advancing whole-brain effective connectivity analysis.