Testing the characteristics of a Lévy process
Testing the characteristics of a Lévy process
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测试 Lévy 过程的特性
DOI：
10.1016/j.spa.2013.03.016
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发表时间：
2013
影响因子：
1.4
通讯作者：
M. Reiß
中科院分区：
文献类型：
--
作者：
M. Reiß
对于Lévy过程在时间距离Δ n处的n个等距观测值，我们考虑了波动率、跳跃测度及其Blumenthal-Getoor指数的非参数或半参数检验问题.当n→∞时，我们渐近地允许高频区Δn= 1 n和低频区Δn=1以及中间情况。通过经验特征函数的方法统一了现有的理论，并揭示了不同的结果。特别强调的是渐近分离率，揭示了这些基本的复杂性，但令人惊讶的非标准推理问题。
For n equidistant observations of a Lévy process at time distance Δnwe consider the problem of testing hypotheses on the volatility, the jump measure and its Blumenthal–Getoor index in a non- or semiparametric manner. Asymptotically as n→∞ we allow for both, the high-frequency regime Δn=1n and the low-frequency regime Δn=1 as well as intermediate cases. The approach via the empirical characteristic function unifies existing theory and sheds new light on diverse results. Particular emphasis is given to asymptotic separation rates which reveal the complexity of these basic, but surprisingly non-standard inference questions.