Conditional independence testing with a single realization of a multivariate nonstationary nonlinear time series

Fuente: arXiv
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Auteurs principaux: Wieck-Sosa, Michael, Haddad, Michel F. C., Ramdas, Aaditya
Format: Preprint
Publié: 2025
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author Wieck-Sosa, Michael
Haddad, Michel F. C.
Ramdas, Aaditya
author_facet Wieck-Sosa, Michael
Haddad, Michel F. C.
Ramdas, Aaditya
contents Identifying relationships among stochastic processes is a core objective in many fields, such as economics. While the standard toolkit for multivariate time series analysis has many advantages, it can be difficult to capture nonlinear dynamics using linear vector autoregressive models. This difficulty has motivated the development of methods for causal discovery and variable selection for nonlinear time series, which routinely employ tests for conditional independence. In this paper, we introduce the first framework for conditional independence testing that works with a single realization of a nonstationary nonlinear process. We also show how our framework can be used to test for independence. The key technical ingredients of our framework are time-varying nonlinear regression, estimation of local long-run covariance matrices of products of error processes, and a distribution-uniform strong Gaussian approximation.
format Preprint
id arxiv_https___arxiv_org_abs_2504_21647
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Conditional independence testing with a single realization of a multivariate nonstationary nonlinear time series
Wieck-Sosa, Michael
Haddad, Michel F. C.
Ramdas, Aaditya
Methodology
Statistics Theory
Machine Learning
Identifying relationships among stochastic processes is a core objective in many fields, such as economics. While the standard toolkit for multivariate time series analysis has many advantages, it can be difficult to capture nonlinear dynamics using linear vector autoregressive models. This difficulty has motivated the development of methods for causal discovery and variable selection for nonlinear time series, which routinely employ tests for conditional independence. In this paper, we introduce the first framework for conditional independence testing that works with a single realization of a nonstationary nonlinear process. We also show how our framework can be used to test for independence. The key technical ingredients of our framework are time-varying nonlinear regression, estimation of local long-run covariance matrices of products of error processes, and a distribution-uniform strong Gaussian approximation.
title Conditional independence testing with a single realization of a multivariate nonstationary nonlinear time series
topic Methodology
Statistics Theory
Machine Learning
url https://arxiv.org/abs/2504.21647