Annals of Statistics
- Ann. Statist.
- Volume 48, Number 2 (2020), 1143-1167.
High-frequency analysis of parabolic stochastic PDEs
We consider the problem of estimating stochastic volatility for a class of second-order parabolic stochastic PDEs. Assuming that the solution is observed at high temporal frequency, we use limit theorems for multipower variations and related functionals to construct consistent nonparametric estimators and asymptotic confidence bounds for the integrated volatility process. As a byproduct of our analysis, we also obtain feasible estimators for the regularity of the spatial covariance function of the noise.
Ann. Statist., Volume 48, Number 2 (2020), 1143-1167.
Received: June 2018
Revised: March 2019
First available in Project Euclid: 26 May 2020
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Chong, Carsten. High-frequency analysis of parabolic stochastic PDEs. Ann. Statist. 48 (2020), no. 2, 1143--1167. doi:10.1214/19-AOS1841. https://projecteuclid.org/euclid.aos/1590480049
- Supplement to “High-frequency analysis of parabolic stochastic PDEs”. This paper is accompanied by supplementary material in . Section A in  gives some auxiliary results needed for the proofs in this paper. In Section B, some important estimates related to the heat kernel are derived. Sections C and D provide the details for the proof of Theorems 2.1 and 2.3, respectively. Finally, Section E contains the proofs for Sections 2.2 and 2.3.