The local fractional bootstrap
提出一种针对布朗半平稳过程高频统计的自举方法，用于检验样本路径的粗糙度，通过模拟辅助分数布朗运动改进有限样本性能，并应用于资产价格和大气湍流数据。
Abstract 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.