Bull, Adam D. Estimating time-changes in noisy Lévy models. (English) Zbl 1305.62387 Ann. Stat. 42, No. 5, 2026-2057 (2014). Summary: In quantitative finance, we often model asset prices as a noisy Itō semimartingale. As this model is not identifiable, approximating by a time-changed Lévy process can be useful for generative modelling. We give a new estimate of the normalised volatility or time change in this model, which obtains minimax convergence rates, and is unaffected by infinite-variation jumps. In the semimartingale model, our estimate remains accurate for the normalised volatility, obtaining convergence rates as good as any previously implied in the literature. Cited in 6 Documents MSC: 62P20 Applications of statistics to economics 62G08 Nonparametric regression and quantile regression 62G20 Asymptotic properties of nonparametric inference 62G35 Nonparametric robustness Keywords:Itō semimartingale; Lévy process; microstructure noise; volatility; time-change PDF BibTeX XML Cite \textit{A. D. Bull}, Ann. Stat. 42, No. 5, 2026--2057 (2014; Zbl 1305.62387) Full Text: DOI arXiv OpenURL