2015/01/30 by Markus Bibinger, Bibinger, Markus, Moritz Jirak +3
Economics, Econometrics and Finance · Mathematics · #62G10 #62M10 #FOS: Mathematics #Statistics Theory (math.ST) #Stochastic processes and financial applications #math.ST #msc:62G10 #msc:62M10 #stat.TH
paper · pdf · doi:10.48550/arxiv.1502.00043
openalex publication_date 2015/01/30 · arxiv created 2016/01/12 · arxiv updated 2016/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This work develops change-point methods for statistics of high-frequency data. The main interest is in the volatility of an Itô semi-martingale, the latter being discretely observed over a fixed time horizon. We construct a minimax-optimal test to discriminate continuous paths from paths comprising volatility jumps. This is embedded into a more general theory to infer the smoothness of volatilities. In a high-frequency framework we prove weak convergence of the test statistic under the hypothesis to an extreme value distribution. Moreover, we develop methods to infer changes in the Hurst parameter of fractional volatility processes. A simulation study demonstrates the practical value in finite-sample applications.