Problem
Research questions and friction points this paper is trying to address.
Granger causality
nonlinear prediction
vector autoregressive models
reproducing kernel Hilbert space (RKHS)
RKHS-Based Inference for Nonlinear Granger Causality via Conditional Centering
🤖 AI Summary
本文提出了一种基于再生核希尔伯特空间（RKHS）的方法，用于检测非线性自回归过程中的非线性格兰杰因果关系，解决了传统方法只能检测线性预测关系的问题。
📝 Abstract
Granger causality is commonly formulated through linear prediction in vector autoregressive models, limiting its ability to detect nonlinear predictive relationships. We propose a reproducing kernel Hilbert space (RKHS)-based test for nonlinear Granger non-causality in conditional mean for nonlinear autoregressive processes. The key idea is a conditional-centering decomposition of the target regression function into an own-history component and an orthogonal component capturing the additional predictive contribution of the potential source history. Non-causality is characterized by the vanishing of the latter component. The own-history component is estimated by kernel ridge regression, and the residuals are embedded in a second RKHS using a conditionally centered kernel. This yields an RKHS-valued residual moment whose squared norm forms the test statistic. We establish a weighted chi-square null limit and consistency against fixed alternatives for the population-centered statistic. An empirically centered version is shown to retain the null limit and enables spectral calibration of critical values and $p$-values without resampling. Simulation studies demonstrate accurate size control and power against nonlinear alternatives, and real-data applications illustrate the usefulness of the method for detecting nonlinear predictive relationships in time series.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Reproducing Kernel Hilbert Space
Nonlinear Granger Causality
Conditional Centering
Kernel Ridge Regression
Spectral Calibration
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