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

Fuente: arXiv
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Main Authors: Heidari, Akram, Podolskij, Mark
Format: Preprint
Published: 2025
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author Heidari, Akram
Podolskij, Mark
author_facet Heidari, Akram
Podolskij, Mark
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2510_12607
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle On goodness-of-fit testing for volatility in McKean-Vlasov models
Heidari, Akram
Podolskij, Mark
Methodology
62E20, 62G10, 60F15, 60H10
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.
title On goodness-of-fit testing for volatility in McKean-Vlasov models
topic Methodology
62E20, 62G10, 60F15, 60H10
url https://arxiv.org/abs/2510.12607