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  • Open Access

Statistical inference on specifying regression models for detecting dependence in autocorrelated series

Feng Chen1, Yu Zhou2,3,*, and Holger Kantz3

  • *Contact author: zhouyu@pks.mpg.de
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Phys. Rev. E 113, 034208 – Published 5 March, 2026

DOI: https://doi.org/10.1103/dv2v-q8tg

Abstract

The traditional regression model for dependence detection has been generalized by including the autocorrelated noise (ACN) or lagged dependent variable (LDV) to account for autocorrelation in time series. Existing studies on specifying the models with ACN or LDV are rare. We propose a statistical analysis framework of model specification and estimation, whose effectiveness is validated by simulations. As real-life cases we study the precipitation extreme dependence on temperature and temperature dependence on CO2 and demonstrate how the traditional and misspecified models may overestimate dependence by up to three times. We provide a solid statistical basis for detecting dependence in autocorrelated series.

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Phys. Rev. E 113, 034208– Published 5 March, 2026
  • Received 2 July 2025
  • Accepted 9 February 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by Max Planck Society.

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