Statistics of discretely observed semi-martingales under noise

Markus Bibinger (HU Berlin)
Wednesday, January 14, 2015 - 10:00am
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

We consider statistical inference with main focus on volatility estimation from discrete noisy observations of a semi-martingale. In the prominent model with market microstructure noise, we discuss asymptotically efficient estimation of the integrated volatility matrix in a multivariate setup under high-frequency asymptotics. The estimation methodology along with stable central limit theorems for a general framework, also in presence of jumps, provide a valid approach for analyzing high-frequency financial data.
The second part of the talk is devoted to a statistical model with irregular noise designed to describe the evolution of intra-day quotes from limit order books. It is demonstrated that this model with order microstructure noise facilitates an improved volatility estimation. We establish the optimal minimax convergence rate.