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arXiv · 2511.22274

Diagnostic Checking for Wasserstein Autoregression

Chenxiao Dai·Feiyu Jiang·Dong Li·Xiaofeng Shao
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Abstract

Wasserstein autoregression provides a robust framework for modeling serial dependence among probability distributions, with wide-ranging applications in economics, finance, and climate science. In this paper, we develop portmanteau-type diagnostic tests for assessing the adequacy of Wasserstein autoregressive models. By defining autocorrelation functions for model errors and residuals in the Wasserstein space, we construct two related tests: one analogous to the classical McLeod type test, and the other based on the sample-splitting approach of Davis and Fernandes(2025). We establish that, under mild regularity conditions, the corresponding test statistics converge in distribution to chi-square limits. Simulation studies and empirical applications demonstrate that the proposed tests effectively detect model mis-specification, offering a principled and reliable diagnostic tool for distributional time series analysis.

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Chenxiao Dai, Feiyu Jiang, Dong Li, Xiaofeng Shao. 2025-11-27. Diagnostic Checking for Wasserstein Autoregression. https://arxiv.org/abs/2511.22274

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