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

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  • 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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    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. Fernandes, Marcelo & Grammig, Joachim, 2003. "A family of autoregressive conditional duration models," Economics Working Papers (Ensaios Economicos da EPGE) 501, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
    3. repec:fth:louvco:2001/36 is not listed on IDEAS
    4. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
    5. 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).
    6. O. Scaillet, 2001. "Density Estimation Using Inverse and Reciprocal Inverse Gaussian Kernels," THEMA Working Papers 2001-24, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    7. Bruce M. Brown, 1999. "Beta-Bernstein Smoothing for Regression Curves with Compact Support," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 26(1), pages 47-59.
    8. 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.
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    Citations

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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. Lemonte, Artur J. & Cribari-Neto, Francisco & Vasconcellos, Klaus L.P., 2007. "Improved statistical inference for the two-parameter Birnbaum-Saunders distribution," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4656-4681, May.
    3. Ané, Thierry & Métais, Carole, 2009. "The distribution of realized variances: Marginal behaviors, asymmetric dependence and contagion effects," International Review of Financial Analysis, Elsevier, vol. 18(3), pages 134-150, June.
    4. 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.
    5. 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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