通过Lamperti变换估计非平稳增量自相似过程的自相似指数
Estimation of the Self-similarity Index of Non-stationary Increments Self-similar Processes via Lamperti Transformations
AI总结：
通过改进的Lamperti变换估计非平稳增量自相似过程的自相似指数，适用于多种分数布朗运动变体，并提供Python实现及实证分析。
摘要：
我们介绍了一种新的方法，用于估计一般$H$-自相似过程的自相似指数，该过程具有平稳或非平稳增量。该估计算法基于一种改进的Lamperti变换，将$H$-自相似过程转换为平稳过程。作为应用，我们展示了如何使用这种方法来估计分数布朗运动、子分数布朗运动、双分数布朗运动和三分数布朗运动的自相似指数。进行了模拟研究以支持我们估计器的一致性。Python实现已公开分享。在900年至1200年间的尼罗河河水位数据上进行了应用。
英文摘要：
We introduce a novel method for estimating the self-similarity index of a general $H$-self-similar process with either stationary or non-stationary increments. The estimation algorithm is developed based on a modified Lamperti transformation, which transforms $H$-self-similar processes to stationary ones. As an application, we show how to use this approach to estimate the self-similarity index of fractional Brownian motion, subfractional Brownian motion, bifractional Brownian motion, and trifractional Brownian motion. Simulation study is performed to support the consistency of our estimators. Implementation in Python is publicly shared. Application on the estimation of the self-similarity index of the Nile river water level data from the year 900 to 1200 C.E..
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