On goodness-of-fit testing for volatility in McKean-Vlasov models
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908592884416512 |
|---|---|
| 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 |