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波动率的非参数变点分析AI 解读

In this work, we develop change-point methods for statistics of high-frequency data. The main interest is in the volatility of an Itô semimartingale, the latter being discretely observed over a fixed time horizon. We construct a minimax-optimal test to discriminate continuous paths from paths with volatility jumps, and it is shown that the test can be embedded into a more general theory to infer the smoothness of volatilities. In a high-frequency setting, we prove weak…

莱维测度与莱维联结函数的非参数推断AI 解读

In this paper nonparametric methods to assess the multivariate Lévy measure are introduced. Starting from high-frequency observations of a Lévy process $\mathbf{X} $, we construct estimators for its tail integrals and the Pareto–Lévy copula and prove weak convergence of these estimators in certain function spaces. Given $n$ observations of increments over intervals of length $\Delta_{n}$, the rate of convergence is $k_{n}^{-1/2}$ for $k_{n}=n\Delta_{n}$ which is natural…

离散观测过程叠加噪声的移动平均极限定理AI 解读

This paper presents some limit theorems for certain functionals of moving averages of semimartingales plus noise which are observed at high frequency. Our method generalizes the pre-averaging approach (see [Bernoulli 15 (2009) 634–658, Stochastic Process. Appl. 119 (2009) 2249–2276]) and provides consistent estimates for various characteristics of general semimartingales. Furthermore, we prove the associated multidimensional (stable) central limit theorems. As expected, we…