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arXiv · 2504.11906

Testing of tempered fractional Brownian motions

Katarzyna Macioszek·Farzad Sabzikar·Krzysztof Burnecki
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Abstract

We propose here a testing methodology based on the autocovariance, detrended moving average, and time-averaged mean-squared displacement statistics for tempered fractional Brownian motions (TFBMs) which are related to the notions of semi-long range dependence and transient anomalous diffusion. In this framework, we consider three types of TFBMs: two with a tempering factor incorporated into their moving-average representation, and one with a tempering parameter added to the autocorrelation formula. We illustrate their dynamics with the use of quantile lines. Using the proposed methodology, we provide a comprehensive power analysis of the tests. It appears that the tests allow distinguishing between the tempered processes with different Hurst parameters.

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Katarzyna Macioszek, Farzad Sabzikar, Krzysztof Burnecki. 2025-04-16. Testing of tempered fractional Brownian motions. https://arxiv.org/abs/2504.11906

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