Asymptotic Normality of Parameter Estimators for~Mixed Fractional Brownian Motion with Trend
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Published:2023-08-15
Issue:SI
Volume:52
Page:127-148
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ISSN:1026-597X
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Container-title:Austrian Journal of Statistics
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language:
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Short-container-title:AJS
Author:
Ralchenko Kostiantyn,Yakovliev Mykyta
Abstract
We investigate the mixed fractional Brownian motion of the form Xt = θt+σWt +κBtH , driven by a standard Brownian motion W and a fractional Brownian motion B H with Hurst parameter H. We consider strongly consistent estimators of unknown model parameters (θ, H, σ, κ) based on the equidistant observations of a trajectory. Joint asymptotic normality of these estimators is proved for H ∈ (0, 12 ).
Publisher
Austrian Statistical Society
Subject
Applied Mathematics,Statistics, Probability and Uncertainty,Statistics and Probability