High-frequency analysis of parabolic stochastic PDEs

By Carsten H. Chong. Annals of Statistics, 2018

55 citations recorded by the source corpus.

We consider the problem of estimating stochastic volatility for a class of second-order parabolic stochastic PDEs. Assuming that the solution is observed at a 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.

Subfields: Finance, Global and Planetary Change

View Paper: https://www.semanticscholar.org/paper/d046ea57ee473559fb562d982b34289eb30a908f

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In Finance

1. Florian Hildebrandt
2. Mathias Trabs
3. Markus Bibinger

In Global and Planetary Change

1. Florian Hildebrandt
2. Markus Bibinger
3. Mathias Trabs

Citations in the corpus

• Volatility estimation for stochastic PDEs using high-frequency observations (2017, methodology): “Chong, C. (2018). High-frequency analysis of parabolic stochastic pdes. arXiv:1806.06959. Cialenco, I. (2018). Statistical inference for spdes: an overview. Statistical Inference for Stochastic Processes, 21(2):309– 329. Cialenco, I. and Glatt-Holtz, N. (2011). Parameter estimation for the stochasti”
• Parameter estimation for SPDEs based on discrete observations in time and space (2019, methodology): “[4] Chong, C. (2019a).”