Quasi-Likelihood Analysis of Fractional Brownian Motion with Constant Drift under High-Frequency Observations

Tetsuya Takabatake

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arXiv · 2206.05126

Quasi-Likelihood Analysis of Fractional Brownian Motion with Constant Drift under High-Frequency Observations

Tetsuya Takabatake

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Abstract

Consider an estimation of the Hurst parameter $H\in(0,1)$ and the volatility parameter $\sigma>0$ for a fractional Brownian motion with a drift term under high-frequency observations with a finite time interval. In the present paper, we propose a consistent estimator of the parameter $\theta=(H,\sigma)$ combining the ideas of a quasi-likelihood function based on a local Gaussian approximation of a high-frequently observed time series and its frequency-domain approximation. Moreover, we prove an asymptotic normality property of the proposed estimator for all $H\in(0,1)$ when the drift process is constant.

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BibTeX RIS

Tetsuya Takabatake. 2022-06-10. Quasi-Likelihood Analysis of Fractional Brownian Motion with Constant Drift under High-Frequency Observations. https://arxiv.org/abs/2206.05126

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