Overview and details of the sessions of this conference. Please select a date or location to show only sessions at that day or location. Please select a single session for detailed view (with abstracts and downloads if available).
Frank van der Meulen1, Daniel Brus2, Moritz Schauer3
1Vrije Universiteit Amsterdam, Netherlands, The; 2ABN-AMRO; 3Chalmers University of Technology & University of Gothenburg
I will discuss a simple example of an interacting particle process which consists of individuals that are either susceptible, infected or recovered. Transitioning from susceptible to infected depends on the number of infected neighbours, causing interaction. I will assume only some individuals at some times can be observed. Can we infer the states of all individuals at all times? The proposed solution is valid in more general settings and if time permits I will comment on that.
11:05am - 11:30am
Nonparametric estimation of the interaction function in particle system models
Denis Belomestny1, Mark Podolskij2, Shi-Yuan Zhou2
1University of Duisburg-Essen, Germany; 2University of Luxembourg, France
This paper delves into a nonparametric estimation approach for the interaction function within diffusion-type particle system models. We introduce two estimation methods based upon an empirical risk minimization. Our study encompasses an analysis of the stochastic and approximation errors associated with both procedures, along with an examination of certain minimax lower bounds.
11:30am - 11:55am
Statistical analysis of a stochastic boundary model for high-frequency data from a limit order book
Markus Bibinger
University of Würzburg, Germany
We propose statistical methods to infer a semi-martingale efficient log-price process in a boundary model with one-sided microstructure noise for high-frequency limit order prices. Two main challenges are to discriminate price jumps from continuous log-price movements and volatility estimation. We develop test and estimation methods and establish asymptotic results in a high-frequency regime. Convergence rates and detection boundaries are shown to hinge on characteristics of the imposed noise distribution. We address the estimation of these noise characteristics and adaptive inference on the semimartingale. For illustration, we shed light on the related asymptotic properties for point estimation of boundary parameters.
11:55am - 12:20pm
Nonparametric Bayesian volatility estimation for gamma-driven stochastic differential equations
Shota Gugushvili
Wageningen University & Research
We consider a nonparametric Bayesian approach to estimation of the volatility function of a stochastic differential equation driven by a gamma process. The volatility function is modelled a priori as piecewise constant, and we specify a gamma prior on its values. This leads to a straightforward MCMC procedure for posterior inference. We give theoretical performance guarantees (minimax optimal contraction rates for the posterior) for the Bayesian estimate in terms of the regularity of the unknown volatility function. We illustrate the method on synthetic and real data examples.
The talk is based on the joint work with D. Belomestny, M. Schauer, and P. Spreij.
