Volatility estimation for stochastic PDEs using highfrequency observations
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Wann 
08.06.2018 von 12:00 bis 13:00 
Wo  ErnstZermeloStraße 1, Raum 404, 4. OG 
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Motivated by random phenomena in natural science
as well as by mathematical finance, stochastic partial differential
equations (SPDEs) have been intensively studied during the last fifty
years with a main focus on theoretical analytic and probabilistic
aspects. Thanks to the exploding number of available data and the fast
progress in information technology, SPDE models become nowadays
increasingly popular for practitioners, for instance, to model neuronal
systems or interest rate fluctuations to give only two examples.
Consequently, statistical methods are required to calibrate this class
of complex models.
We study the parameter estimation for parabolic, linear, second order
SPDEs observing a mild solution on a discrete grid in time and space. A
highfrequency 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 the squared increments of the process. The estimator is
consistent and admits a central limit theorem. This is established
moreover for the estimation of the integrated volatility in a
semiparametric framework. Starting from a representation of the
solution as an infinite factor model and exploiting mixing properties of
Gaussian time series, the theory considerably differs from the
statistics for semimartingales literature. The performance of the
method is illustrated in a simulation study.
This is joint work with Markus Bibinger.