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Least Squares Estimation for α‐Fractional Bridge with Discrete Observations

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  • Guangjun Shen
  • Xiuwei Yin

Abstract

We consider a fractional bridge defined as dXt=-α(Xt/(T-t))dt+dBtH, 0≤t 1/2 and parameter α > 0 is unknown. We are interested in the problem of estimating the unknown parameter α > 0. Assume that the process is observed at discrete time ti = iΔn, i = 0, …, n, and Tn = nΔn denotes the length of the “observation window.” We construct a least squares estimator α∧n of α which is consistent; namely, α∧n converges to α in probability as n → ∞.

Suggested Citation

  • Guangjun Shen & Xiuwei Yin, 2014. "Least Squares Estimation for α‐Fractional Bridge with Discrete Observations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:748376
    DOI: 10.1155/2014/748376
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    References listed on IDEAS

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    1. Hu, Yaozhong & Nualart, David, 2010. "Parameter estimation for fractional Ornstein-Uhlenbeck processes," Statistics & Probability Letters, Elsevier, vol. 80(11-12), pages 1030-1038, June.
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