Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Estimation of Hurst Parameter in Longitudinal Data with Long Memory

  • Kim, Yoon Tae (Department of Finance and Information Statistics, Hallym University) ;
  • Park, Hyun Suk (Department of Finance and Information Statistics, Hallym University)
  • Received : 2015.03.18
  • Accepted : 2015.05.13
  • Published : 2015.05.31
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Abstract

This paper considers the problem of estimation of the Hurst parameter H ${\in}$ (1/2, 1) from longitudinal data with the error term of a fractional Brownian motion with Hurst parameter H that gives the amount of the long memory of its increment. We provide a new estimator of Hurst parameter H using a two scale sampling method based on $A{\ddot{i}}t$-Sahalia and Jacod (2009). Asymptotic behaviors (consistent and central limit theorem) of the proposed estimator will be investigated. For the proof of a central limit theorem, we use recent results on necessary and sufficient conditions for multi-dimensional vectors of multiple stochastic integrals to converges in distribution to multivariate normal distribution studied by Nourdin et al. (2010), Nualart and Ortiz-Latorre (2008), and Peccati and Tudor (2005).

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References

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Cited by

  1. Convergence rate of a test statistics observed by the longitudinal data with long memory vol.24, pp.5, 2017, https://doi.org/10.5351/CSAM.2017.24.5.481