Prof. M. Bibinger (Universität Marburg)
Wednesday, November 21, 2018 - 10:00
Mohrenstr. 39, 10117 Berlin, Weierstraß-Hörsaal (Raum: 406), 4. Etage
Forschungsseminar Mathematische Statistik
In this talk, we review recent contributions on statistical theory to infer path properties of volatility. The interest is in the latent volatility of an It^o semimartingale, the latter being discretely observed over a fixed time horizon. We consider tests to discriminate continuous paths from paths with volatility jumps. Both a local test for jumps at speciied times and a global test for jumps over the whole observation interval are discussed. We establish consistency and optimality properties under infill asymptotics, also for observations with additional additive noise. Recently, there is high interest in the smoothness regularity of the volatility process as confl icting models are proposed in the literature. To address this point, we consider inference on the Hurst exponent of fractional stochastic volatility processes. Even though the regularity of the volatility determines optimal spot volatility estimation methods, forecasting techniques and the volatility persistence, identifiability is an unsolved question in high-frequency statistics. We discuss a first approach which can reveal if path properties are stable over time or changing. Eventually, we discuss some recent considerations and conjectures on this open question. The related easier problem of inference on the Hurst exponent from direct discrete observations of a fractional Brownian motion is also visited.
submitted by chschnei (, 030 20372574)