Volatility change point detection for linear parabolic SPDEs

TL;DR

This paper develops a statistical test for detecting changes in volatility in linear parabolic stochastic partial differential equations using high-frequency data, with proven consistency and asymptotic properties.

Contribution

It introduces a novel change point detection method for volatility in SPDEs, extending change point analysis techniques to complex stochastic PDE models.

Findings

Test statistic derived and its null distribution established

The test is shown to be consistent

Numerical simulations validate the method

Abstract

We consider change point detection for the volatility in second order linear parabolic stochastic partial differential equations based on high frequency spatio-temporal data. We give a test statistic to detect changes in the volatility based on change point analysis for diffusion processes and derive the asymptotic null distribution of the test statistic. We also show that the test is consistent. Moreover, we provide some examples and then perform numerical simulations of the proposed test statistic.