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On the Spectral Density of Fractional Ornstein-Uhlenbeck Processes

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Listed:
  • Shuping Shi

    (Macquarie University)

  • Jun Yu

    (University of Macau)

  • Chen Zhang

    (University of Macau)

Abstract

This paper introduces a novel and easy-to-implement method for accurately approximating the spectral density of discretely sampled fractional Ornstein-Uhlenbeck (fOU) processes. The method offers a substantial reduction in approximation error, particularly within the rough region of the fractional parameter H 2 (0;0:5). This approximate spectral density has the potential to enhance the performance of estimation methods and hypothesis testing that make use of spectral densities. We introduce the approximate Whittle maximum likelihood (AWML) method for discretely sampled fOU processes, utilising the approximate spectral density, and demonstrate that the AWML estimator exhibits properties of consistency and asymptotic normality when H 2 (0;1), akin to the conventional Whittle maximum likelihood method. Through extensive simulation studies, we show that AWML outperforms existing methods in terms of estimation accuracy in finite samples. We then apply the AWML method to the trading volume of 40 financial assets. Our empirical findings reveal that the estimated Hurst parameters for these assets fall within the range of 0:10 to 0:21, indicating a rough dynamic.

Suggested Citation

  • Shuping Shi & Jun Yu & Chen Zhang, 2024. "On the Spectral Density of Fractional Ornstein-Uhlenbeck Processes," Working Papers 202416, University of Macau, Faculty of Business Administration.
    • Handle: RePEc:boa:wpaper:202416
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    References listed on IDEAS

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    More about this item

    Keywords

    Fractional Brownian motion; Fractional Ornstein-Uhlenbeck process; Spectral density; Paxson approximation; Whittle maximum likelihood; Realized volatility;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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