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Birnbaum-Saunders and Lognormal Kernel Estimators for Modelling Durations in High Frequency Financial Data

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Author Info

  • Xiaodong Jin

    ()
    (Department of Mathematics, UNC at Charlotte)

  • Janusz Kawczak

    ()
    (Department of Mathematics, UNC at Charlotte)

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    Abstract

    In this article we extend the class of non-negative, asymmetric kernel density estimators and propose Birnbaum-Saunders (BS) and lognormal (LN) kernel density functions. The density functions have bounded support on [0,1). Both BS and LN kernel estimators are free of boundary bias, non-negative, with natural varying shape, and achieve the optimal rate of convergence for the mean integrated squared error. We apply BS and LN kernel density estimators to high frequency intraday time duration data. The comparisons are made on several nonparametric kernel density estimators. BS and LN kernels perform better near the boundary in terms of bias reduction.

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    File URL: http://www.aeconf.net/Articles/May2003/aef040106.pdf
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    Bibliographic Info

    Article provided by Society for AEF in its journal Annals of Economics and Finance.

    Volume (Year): 4 (2003)
    Issue (Month): 1 (May)
    Pages: 103-124

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    Handle: RePEc:cuf:journl:y:2003:v:4:i:1:p:103-124

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    Related research

    Keywords: Birnbaum-Saunders kernel; Lognormal kernel; High frequency; ACD model; Durations;

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    References

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    1. Fernandes, M. & Grammig, J., 2000. "Non-Parametric Specification Tests for Conditional Duration Models," Economics Working Papers eco2000/4, European University Institute.
    2. Olivier SCAILLET, 2001. "Density Estimation Using Inverse and Reciprocal Inverse Guassian Kernels," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2001017, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    3. Fernandes, Marcelo & Grammig, Joachim, 2006. "A family of autoregressive conditional duration models," Journal of Econometrics, Elsevier, vol. 130(1), pages 1-23, January.
    4. GIOT, Pierre, 1999. "Time transformations, intraday data and volatility models," CORE Discussion Papers 1999044, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Song Chen, 2000. "Probability Density Function Estimation Using Gamma Kernels," Annals of the Institute of Statistical Mathematics, Springer, vol. 52(3), pages 471-480, September.
    6. repec:fth:louvco:2001/36 is not listed on IDEAS
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    Cited by:
    1. Hirukawa, Masayuki & Sakudo, Mari, 2014. "Nonnegative bias reduction methods for density estimation using asymmetric kernels," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 112-123.
    2. Marchant, Carolina & Bertin, Karine & Leiva, Víctor & Saulo, Helton, 2013. "Generalized Birnbaum–Saunders kernel density estimators and an analysis of financial data," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 1-15.
    3. Igarashi, Gaku & Kakizawa, Yoshihide, 2014. "Re-formulation of inverse Gaussian, reciprocal inverse Gaussian, and Birnbaum–Saunders kernel estimators," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 235-246.

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