A1413
Title: Change detection for the volatility in linear parabolic SPDEs
Authors: Yozo Tonaki - The University of Osaka (Japan) [presenting]
Yusuke Kaino - Kobe University (Japan)
Masayuki Uchida - The University of Osaka and University of Tokyo (Japan)
Abstract: Volatility change point detection is considered for second order linear parabolic stochastic partial differential equations (SPDEs) based on high frequency spatio-temporal data. Ornstein-Uhlenbeck processes can be obtained from the inner product of the solution of the SPDE and an orthonormal system, and these processes can be approximated through statistical inference for SPDEs based on high frequency spatio-temporal data. A test statistic is thus proposed to detect changes of the volatility function over time based on change point analysis for diffusion processes, and the asymptotic null distribution of the proposed test statistic is derived. The proposed test is then shown to be consistent. Additionally, some examples are provided and numerical simulations of the proposed test statistic are performed.
