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Generalized Birnbaum–Saunders kernel density estimators and an analysis of financial data

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  • Marchant, Carolina
  • Bertin, Karine
  • Leiva, Víctor
  • Saulo, Helton

Abstract

The kernel method is a nonparametric procedure used to estimate densities with support in R. When nonnegative data are modeled, the classical kernel density estimator presents a bias problem in the neighborhood of zero. Several methods have been developed to reduce this bias, which include the boundary kernel, data transformation and reflection methods. An alternative proposal is to use kernel estimators based on distributions with nonnegative support, as is the case of the Birnbaum–Saunders (BS), gamma, inverse Gaussian and lognormal models. Generalized BS (GBS) distributions have received considerable attention, due to their properties and their flexibility in modeling different types of data. In this paper, we propose, characterize and implement the kernel method based on GBS distributions to estimate densities with nonnegative support. In addition, we provide a simple method to choose the corresponding bandwidth. In order to evaluate the performance of these new estimators, we conduct a Monte Carlo simulation study. The obtained results are illustrated by analyzing financial real data.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:63:y:2013:i:c:p:1-15
    DOI: 10.1016/j.csda.2013.01.013
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    1. Barros, Michelli & Paula, Gilberto A. & Leiva, Víctor, 2009. "An R implementation for generalized Birnbaum-Saunders distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1511-1528, February.
    2. Bouezmarni, Taoufik & Rombouts, Jeroen V.K., 2010. "Nonparametric density estimation for positive time series," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 245-261, February.
    3. Gilberto A. Paula & Víctor Leiva & Michelli Barros & Shuangzhe Liu, 2012. "Robust statistical modeling using the Birnbaum‐Saunders‐t distribution applied to insurance," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 28(1), pages 16-34, January.
    4. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643.
    5. McInish, Thomas H & Wood, Robert A, 1992. "An Analysis of Intraday Patterns in Bid/Ask Spreads for NYSE Stocks," Journal of Finance, American Finance Association, vol. 47(2), pages 753-764, June.
    6. Leiva, Victor & Barros, Michelli & Paula, Gilberto A. & Galea, Manuel, 2007. "Influence diagnostics in log-Birnbaum-Saunders regression models with censored data," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5694-5707, August.
    7. Xiaodong Jin & Janusz Kawczak, 2003. "Birnbaum-Saunders and Lognormal Kernel Estimators for Modelling Durations in High Frequency Financial Data," Annals of Economics and Finance, Society for AEF, vol. 4(1), pages 103-124, May.
    8. Thomas H. McInish & Robert A. Wood, 1991. "Hourly Returns, Volume, Trade Size, And Number Of Trades," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 14(4), pages 303-315, December.
    9. Marcelo Fernandes & Paulo Monteiro, 2005. "Central limit theorem for asymmetric kernel functionals," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(3), pages 425-442, September.
    10. Robert F. Engle, 2000. "The Econometrics of Ultra-High Frequency Data," Econometrica, Econometric Society, vol. 68(1), pages 1-22, January.
    11. Song Chen, 2000. "Probability Density Function Estimation Using Gamma Kernels," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(3), pages 471-480, September.
    12. Hubert, M. & Vandervieren, E., 2008. "An adjusted boxplot for skewed distributions," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5186-5201, August.
    13. Chen, Song Xi, 1999. "Beta kernel estimators for density functions," Computational Statistics & Data Analysis, Elsevier, vol. 31(2), pages 131-145, August.
    14. Vilca, Filidor & Santana, Lucia & Leiva, Víctor & Balakrishnan, N., 2011. "Estimation of extreme percentiles in Birnbaum-Saunders distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1665-1678, April.
    15. Jan Johannes & Suhasini Rao, 2011. "Nonparametric estimation for dependent data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(3), pages 661-681.
    16. Leiva, Victor & Riquelme, Marco & Balakrishnan, N. & Sanhueza, Antonio, 2008. "Lifetime analysis based on the generalized Birnbaum-Saunders distribution," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 2079-2097, January.
    17. Lejeune, Michel & Sarda, Pascal, 1992. "Smooth estimators of distribution and density functions," Computational Statistics & Data Analysis, Elsevier, vol. 14(4), pages 457-471, November.
    18. Thomas H. McInish & Robert A. Wood, 1991. "Hourly Returns, Volume, Trade Size, And Number Of Trades," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 14(4), pages 303-315, December.
    19. Zhang, Michael Yuanjie & Russell, Jeffrey R. & Tsay, Ruey S., 2001. "A nonlinear autoregressive conditional duration model with applications to financial transaction data," Journal of Econometrics, Elsevier, vol. 104(1), pages 179-207, August.
    20. Abadir, Karim M. & Lawford, Steve, 2004. "Optimal asymmetric kernels," Economics Letters, Elsevier, vol. 83(1), pages 61-68, April.
    21. Peter Diggle, 1985. "A Kernel Method for Smoothing Point Process Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 34(2), pages 138-147, June.
    22. Azevedo, Cecilia & Leiva, Víctor & Athayde, Emilia & Balakrishnan, N., 2012. "Shape and change point analyses of the Birnbaum–Saunders-t hazard rate and associated estimation," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3887-3897.
    23. Bhatti, Chad R., 2010. "The Birnbaum–Saunders autoregressive conditional duration model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(10), pages 2062-2078.
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    2. Célestin C. Kokonendji & Sobom M. Somé, 2021. "Bayesian Bandwidths in Semiparametric Modelling for Nonnegative Orthant Data with Diagnostics," Stats, MDPI, vol. 4(1), pages 1-22, March.
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    5. Danúbia R. Cunha & Roberto Vila & Helton Saulo & Rodrigo N. Fernandez, 2020. "A General Family of Autoregressive Conditional Duration Models Applied to High-Frequency Financial Data," JRFM, MDPI, vol. 13(3), pages 1-20, March.
    6. Yasmina Ziane & Nabil Zougab & Smail Adjabi, 2018. "Birnbaum–Saunders power-exponential kernel density estimation and Bayes local bandwidth selection for nonnegative heavy tailed data," Computational Statistics, Springer, vol. 33(1), pages 299-318, March.
    7. Kakizawa, Yoshihide, 2021. "A class of Birnbaum–Saunders type kernel density estimators for nonnegative data," Computational Statistics & Data Analysis, Elsevier, vol. 161(C).
    8. Ouimet, Frédéric & Tolosana-Delgado, Raimon, 2022. "Asymptotic properties of Dirichlet kernel density estimators," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    9. Gaku Igarashi, 2016. "Bias reductions for beta kernel estimation," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(1), pages 1-30, March.
    10. Gaku Igarashi, 2018. "Multivariate Density Estimation Using a Multivariate Weighted Log-Normal Kernel," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(2), pages 247-266, August.
    11. Malec, Peter & Schienle, Melanie, 2014. "Nonparametric kernel density estimation near the boundary," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 57-76.
    12. Kakizawa, Yoshihide, 2022. "Multivariate elliptical-based Birnbaum–Saunders kernel density estimation for nonnegative data," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
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    15. Ziane Yasmina & Zougab Nabil & Adjabi Smail, 2021. "Body tail adaptive kernel density estimation for nonnegative heavy-tailed data," Monte Carlo Methods and Applications, De Gruyter, vol. 27(1), pages 57-69, March.

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