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

This paper develops a statistical framework for goodness-of-fit testing of volatility functions in McKean-Vlasov stochastic differential equations, which describe large systems of interacting particles with distribution-dependent dynamics. While integrated volatility estimation in classical SDEs is now well established, formal model validation and goodness-of-fit testing for McKean-Vlasov systems remain largely unexplored, particularly in regimes with both large particle limits and high-frequency sampling. We propose a test statistic based on discrete observations of particle systems, analysed in a joint regime where both the number of particles and the sampling frequency increase. The estimators involved are proven to be consistent, and the test statistic is shown to satisfy a central limit theorem, converging in distribution to a centred Gaussian law.