Estimation of the Self-similarity Index of Non-stationary Increments Self-similar Processes via Lamperti Transformations

William Wu; Qidi Peng

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arXiv · 2602.21764

Estimation of the Self-similarity Index of Non-stationary Increments Self-similar Processes via Lamperti Transformations

William Wu·Qidi Peng

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Abstract

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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William Wu, Qidi Peng. 2026-02-25. Estimation of the Self-similarity Index of Non-stationary Increments Self-similar Processes via Lamperti Transformations. https://arxiv.org/abs/2602.21764

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