Diagnostic Checking for Wasserstein Autoregression
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.
Cite
@article{arxiv.2511.22274,
title = {Diagnostic Checking for Wasserstein Autoregression},
author = {Chenxiao Dai and Feiyu Jiang and Dong Li and Xiaofeng Shao},
journal= {arXiv preprint arXiv:2511.22274},
year = {2025}
}