On goodness-of-fit testing for volatility in McKean-Vlasov models

Akram Heidari; Mark Podolskij

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arXiv · 2510.12607

On goodness-of-fit testing for volatility in McKean-Vlasov models

Akram Heidari·Mark Podolskij

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Abstract

This paper develops a statistical framework for goodness-of-fit testing of volatility functions in i.i.d. McKean-Vlasov stochastic differential equations, which model large diffusion systems with distribution-dependent dynamics. Although integrated volatility estimation for classical SDEs is well established, formal model validation and goodness-of-fit testing for McKean-Vlasov systems remain largely unexplored, particularly in settings combining large particle limits with high-frequency observations. We propose a goodness-of-fit test based on discrete observations of a particle system and study its asymptotic properties in a joint regime where both the number of particles and the sampling frequency tend to infinity. We establish asymptotic normality for the relevant volatility estimators and derive a central limit theorem for the resulting test statistic. These results provide a rigorous basis for assessing volatility specifications in high-dimensional mean-field diffusion models.

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Akram Heidari, Mark Podolskij. 2025-10-14. On goodness-of-fit testing for volatility in McKean-Vlasov models. https://arxiv.org/abs/2510.12607

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