Volatility estimation for stochastic PDEs using high-frequency observations
By Markus Bibinger, Mathias Trabs. Stochastic Processes and their Applications, 2017
62 citations recorded by the source corpus.
We study the parameter estimation for parabolic, linear, second-order, stochastic partial differential equations (SPDEs) observing a mild solution on a discrete grid in time and space. A high-frequency regime is considered where the mesh of the grid in the time variable goes to zero. Focusing on volatility estimation, we provide an explicit and easy to implement method of moments estimator based on squared increments. The estimator is consistent and admits a central limit theorem. This is established moreover for the joint estimation of the integrated volatility and parameters in the differential operator in a semi-parametric framework. Starting from a representation of the solution of the SPDE with Dirichlet boundary conditions as an infinite factor model and exploiting mixing-type properties of time series, the theory considerably differs from the statistics for semi-martingales literature. The performance of the method is illustrated in a simulation study.
Subfields: Finance, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/cfa804faa1c7e4390bc9913793b6ade69d9131f6
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Citations in the corpus
- Parameter estimation for SPDEs based on discrete observations in time and space (2019, methodology): “For the stochastic heat equation it is observed in [3] that a central limit theorem for realized temporal quadratic variations requires that the observation”