英文标题：
《Semiparametric inference on the fractal index of Gaussian and
conditionally Gaussian time series data》
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作者：
Mikkel Bennedsen
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最新提交年份：
2018
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英文摘要：
We study a well-known estimator of the fractal index of a stochastic process. Our framework is very general and encompasses many models of interest; we show how to extend the theory of the estimator to a large class of non-Gaussian processes. Particular focus is on clarity and ease of implementation of the estimator and the associated asymptotic results, making it easy for practitioners to apply the methods. We additionally show how measurement noise in the observations will bias the estimator, potentially resulting in the practitioner 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. Finally, the methods are illustrated on two empirical data sets; one of turbulent velocity flows and one of financial prices.
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中文摘要：
我们研究了一个著名的随机过程分形指数的估计。我们的框架非常通用，包含许多感兴趣的模型；我们展示了如何将估计量理论推广到一大类非高斯过程。特别关注估值器和相关渐近结果的清晰性和易实现性，使从业者能够轻松应用这些方法。此外，我们还展示了观测值中的测量噪声如何使估计器产生偏差，从而可能导致从业者错误地发现时间序列中分形特征的证据。我们提出了一种对这种噪声具有鲁棒性的新估计量，并对观测值中是否存在噪声进行了形式化假设检验。最后，在两个实证数据集上对这些方法进行了说明；一个是动荡的速度流，另一个是金融价格。
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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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