Detecting Nonlinear Causality in Multivariate Time Series with Sparse Additive Models

TL;DR

This paper introduces a nonparametric approach using sparse additive models to detect nonlinear causal relationships in multivariate time series, supported by theoretical analysis and an efficient algorithm.

Contribution

It develops a novel nonparametric method with theoretical guarantees for causal detection in multivariate time series using sparse additive models.

Findings

The method can accurately identify nonlinear causal relationships.

The proposed algorithm converges linearly with high probability.

Theoretical analysis confirms the estimator's statistical properties.

Abstract

We propose a nonparametric method for detecting nonlinear causal relationship within a set of multidimensional discrete time series, by using sparse additive models (SpAMs). We show that, when the input to the SpAM is a $\beta$-mixing time series, the model can be fitted by first approximating each unknown function with a linear combination of a set of B-spline bases, and then solving a group-lasso-type optimization problem with nonconvex regularization. Theoretically, we characterize the oracle statistical properties of the proposed sparse estimator in function estimation and model selection. Numerically, we propose an efficient pathwise iterative shrinkage thresholding algorithm (PISTA), which tames the nonconvexity and guarantees linear convergence towards the desired sparse estimator with high probability.