Diagnostic Checking for Wasserstein Autoregression

2025-11-27

AI Summary

Existing Wasserstein autoregressive models for distributional time series lack formal diagnostic tools for assessing model adequacy. Method: This paper establishes the first diagnostic testing framework in the Wasserstein space: it defines a residual Wasserstein autocorrelation function based on optimal transport and proposes two Portmanteau-type test statistics; integrating McLeod–Li test principles with sample-splitting strategies, it ensures the asymptotic chi-squared distribution of the statistics under mild regularity conditions. Contribution/Results: Simulation and empirical studies demonstrate that the proposed method significantly improves detection power against model misspecification—including omitted dynamic structure and incorrect autoregressive order—while exhibiting strong statistical power and robustness. This work fills a critical theoretical gap in diagnostic methodology for distributional time series modeling and provides the first rigorous, implementable sufficiency test for Wasserstein autoregression.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Knowledge Representation and Reasoning: Diagnosis and Abductive Reasoning
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

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.

Problem

• Develop diagnostic tests for Wasserstein autoregressive models
• Assess model adequacy via autocorrelation in Wasserstein space
• Detect mis-specification in distributional time series analysis

Innovation

• Develops portmanteau-type diagnostic tests for Wasserstein autoregression
• Defines autocorrelation functions for errors in Wasserstein space
• Constructs tests based on McLeod type and sample-splitting approach