Semiparametric estimation and inference on the fractal index of Gaussian and conditionally Gaussian time series data
研究了时间序列分形指数估计量受测量噪声（如微观结构噪声）影响的问题，提出了一种对噪声稳健的新估计量，并构建了噪声存在性的假设检验，通过模拟和实证数据（湍流速度流和金融价格）验证了方法。
This paper studies the properties of a particular estimator of the fractal index of a time series with a view to applications in financial econometrics and mathematical finance. We show how measurement noise (e.g., microstructure noise) in the observations will bias the estimator, potentially resulting in the econometrician erroneously finding evidence of fractal characteristics in a time series. We propose a new estimator which is robust to such noise and construct a formal hypothesis test for the presence of noise in the observations. A number of simulation exercises are carried out, providing guidance for implementation of the theory. Finally, the methods are illustrated on two empirical data sets; one of turbulent velocity flows and one of financial prices.