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Main Authors:	Wu, William, Peng, Qidi
Format:	Preprint
Published:	2026
Subjects:	Statistics Theory 60G18, 60G22, 65C10
Online Access:	https://arxiv.org/abs/2602.21764
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author	Wu, William Peng, Qidi
author_facet	Wu, William Peng, Qidi
contents	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..
format	Preprint
id	arxiv_https___arxiv_org_abs_2602_21764
institution	arXiv
publishDate	2026
record_format	arxiv
spellingShingle	Estimation of the Self-similarity Index of Non-stationary Increments Self-similar Processes via Lamperti Transformations Wu, William Peng, Qidi Statistics Theory 60G18, 60G22, 65C10 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..
title	Estimation of the Self-similarity Index of Non-stationary Increments Self-similar Processes via Lamperti Transformations
topic	Statistics Theory 60G18, 60G22, 65C10
url	https://arxiv.org/abs/2602.21764

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