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Statistical inference in discretely observed fractional Ornstein–Uhlenbeck processes

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  • Li, Yicun
  • Teng, Yuanyang

Abstract

In this paper, we develop a two-stage method for estimating all the unknown parameters in the fractional Ornstein–Uhlenbeck model from discrete observations. The estimation procedure is built upon the marriage of the power variation and the minimum contrast estimation. In the first stage, the Hurst coefficient is estimated by the increment Bernoulli statistic and the volatility parameter is estimated by power variations. The asymptotic theory of the proposed estimators in the diffusion term are established under an in-fill asymptotic scheme. In the second stage, two drift parameters are estimated based on the minimum contrast estimation. Their asymptotic theory are analyzed via use of a double asymptotic scheme. The results from Monte Carlo studies illustrate that the proposed estimators have reasonable finite sample properties. An empirical illustration based on realized volatility indicates that the realized volatility is rough.

Suggested Citation

  • Li, Yicun & Teng, Yuanyang, 2023. "Statistical inference in discretely observed fractional Ornstein–Uhlenbeck processes," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    • Handle: RePEc:eee:chsofr:v:177:y:2023:i:c:s0960077923011050
    DOI: 10.1016/j.chaos.2023.114203
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    Keywords

    Fractional Brownian motion; Increment ratio statistic; Power variation; Minimum contrast estimation; In-fill asymptotics; Double asymptotics;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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