英文标题：
《The Local Fractional Bootstrap》
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作者：
Mikkel Bennedsen and Ulrich Hounyo and Asger Lunde and Mikko S.
Pakkanen
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最新提交年份：
2017
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英文摘要：
We introduce a bootstrap procedure for high-frequency statistics of Brownian semistationary processes. More specifically, we focus on a hypothesis test on the roughness of sample paths of Brownian semistationary processes, which uses an estimator based on a ratio of realized power variations. Our new resampling method, the local fractional bootstrap, relies on simulating an auxiliary fractional Brownian motion that mimics the fine properties of high frequency differences of the Brownian semistationary process under the null hypothesis. We prove the first order validity of the bootstrap method and in simulations we observe that the bootstrap-based hypothesis test provides considerable finite-sample improvements over an existing test that is based on a central limit theorem. This is important when studying the roughness properties of time series data; we illustrate this by applying the bootstrap method to two empirical data sets: we assess the roughness of a time series of high-frequency asset prices and we test the validity of Kolmogorov\'s scaling law in atmospheric turbulence data.
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中文摘要：
我们介绍了布朗半平稳过程高频统计的一个bootstrap过程。更具体地说，我们关注布朗半平稳过程样本路径粗糙度的假设检验，它使用基于已实现功率变化比率的估计。我们的新重采样方法局部分数bootstrap依赖于模拟一个辅助分数布朗运动，该运动模拟了零假设下布朗半平稳过程高频差的精细性质。我们证明了bootstrap方法的一阶有效性，并在模拟中观察到，基于bootstrap的假设检验比基于中心极限定理的现有检验提供了相当大的有限样本改进。这在研究时间序列数据的粗糙度特性时很重要；我们通过将bootstrap方法应用于两个经验数据集来说明这一点：我们评估了高频资产价格时间序列的粗糙度，并在大气湍流数据中检验了科尔莫戈罗夫标度定律的有效性。
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分类信息：

一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Quantitative Finance 数量金融学
二级分类：Statistical Finance 统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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