Detecting Nonlinear Causality in Multivariate Time Series with Sparse Additive Models
This work addresses causality detection in time series for fields like economics or neuroscience, but it appears incremental as it builds on existing sparse additive models with nonconvex regularization.
The authors tackled the problem of detecting nonlinear causal relationships in multivariate time series by proposing a nonparametric method using sparse additive models (SpAMs), achieving theoretical oracle properties and an efficient algorithm with linear convergence.
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 $β$-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.