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Nonparametric density estimation for positive time series

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  • Bouezmarni, Taoufik
  • Rombouts, Jeroen V.K.

Abstract

The Gaussian kernel density estimator is known to have substantial problems for bounded random variables with high density at the boundaries. For independent and identically distributed data, several solutions have been put forward to solve this boundary problem. In this paper, we propose the gamma kernel estimator as a density estimator for positive time series data from a stationary [alpha]-mixing process. We derive the mean (integrated) squared error and asymptotic normality. In a Monte Carlo simulation, we generate data from an autoregressive conditional duration model and a stochastic volatility model. We study the local and global behavior of the estimator and we find that the gamma kernel estimator outperforms the local linear density estimator and the Gaussian kernel estimator based on log-transformed data. We also illustrate the good performance of the h-block cross-validation method as a bandwidth selection procedure. An application to data from financial transaction durations and realized volatility is provided.

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Bibliographic Info

Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

Volume (Year): 54 (2010)
Issue (Month): 2 (February)
Pages: 245-261

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Handle: RePEc:eee:csdana:v:54:y:2010:i:2:p:245-261

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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  1. Meitz, Mika & Saikkonen, Pentti, 2008. "Ergodicity, Mixing, And Existence Of Moments Of A Class Of Markov Models With Applications To Garch And Acd Models," Econometric Theory, Cambridge University Press, vol. 24(05), pages 1291-1320, October.
  2. 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.
  3. BAUWENS, Luc & VEREDAS, David, 1999. "The stochastic conditional duration model: a latent factor model for the analysis of financial durations," CORE Discussion Papers 1999058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Federico M. Bandi & Peter C. B. Phillips, 2003. "Fully Nonparametric Estimation of Scalar Diffusion Models," Econometrica, Econometric Society, vol. 71(1), pages 241-283, January.
  5. Niels Haldrup & Morten O. Nielsen, 2004. "A Regime Switching Long Memory Model for Electricity Prices," Economics Working Papers 2004-2, School of Economics and Management, University of Aarhus.
  6. Fernandes, Marcelo & Grammig, Joachim, 2002. "A Family of Autoregressive Conditional Duration Models," Economics Working Papers (Ensaios Economicos da EPGE) 440, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  7. BAUWENS , Luc & GIOT, Pierre & GRAMMIG, Joachim & VEREDAS, David, 2000. "A comparison of financial duration models via density forecasts," CORE Discussion Papers 2000060, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  8. BAUWENS, Luc & VEREDAS, David, . "The stochastic conditional duration model: a latent variable model for the analysis of financial durations," CORE Discussion Papers RP -1688, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  9. BAUWENS, Luc & HAUTSCH, Nikolaus, . "Stochastic conditional intensity processes," CORE Discussion Papers RP -1937, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  10. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
  11. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  12. Fernandes, M., 2000. "Central Limit Theorem for Asymmetric Kernel Functionals," Economics Working Papers eco2000/1, European University Institute.
  13. Lejeune, Michel & Sarda, Pascal, 1992. "Smooth estimators of distribution and density functions," Computational Statistics & Data Analysis, Elsevier, vol. 14(4), pages 457-471, November.
  14. Ole E. Barndorff-Nielsen & Neil Shephard, 2000. "Econometric analysis of realised volatility and its use in estimating stochastic volatility models," Economics Papers 2001-W4, Economics Group, Nuffield College, University of Oxford, revised 05 Jul 2001.
  15. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001. "Modeling and Forecasting Realized Volatility," NBER Working Papers 8160, National Bureau of Economic Research, Inc.
  16. David A. Chapman & Neil D. Pearson, 1998. "Is the Short Rate Drift Actually Nonlinear?," Finance 9808005, EconWPA.
  17. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(01), pages 17-39, February.
  18. Marcelo Fernandes & Joachim Grammig, 2000. "Non-Parametric Specification Tests For Conditional Duration Models," Computing in Economics and Finance 2000 40, Society for Computational Economics.
  19. Drost, F.C. & Werker, B.J.M., 2001. "Semiparametric Duration Models," Discussion Paper 2001-11, Tilburg University, Center for Economic Research.
  20. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643, October.
  21. Chen, Song Xi, 1999. "Beta kernel estimators for density functions," Computational Statistics & Data Analysis, Elsevier, vol. 31(2), pages 131-145, August.
  22. Song Chen, 2002. "Local Linear Smoothers Using Asymmetric Kernels," Annals of the Institute of Statistical Mathematics, Springer, vol. 54(2), pages 312-323, June.
  23. 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.
  24. Park, B.U. & Simar, L., 1992. "Efficient Semiparametric Estimation in Stochastic Frontier Model," Papers 9201, Catholique de Louvain - Institut de statistique.
  25. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
  26. Matthias Hagmann & Olivier Scaillet, 2004. "Local Multiplicative Bias Correction For Asymmetric Kernel Density Estimators," Royal Economic Society Annual Conference 2004 25, Royal Economic Society.
  27. Hardle, W., 1992. "Applied Nonparametric Methods," Papers 9204, Catholique de Louvain - Institut de statistique.
  28. James D. Hamilton & Oscar Jorda, 2000. "A Model for the Federal Funds Rate Target," NBER Working Papers 7847, National Bureau of Economic Research, Inc.
  29. 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).
  30. Eric Ghysels & Christian Gourieroux & Joanna Jasiak, 1997. "Stochastic Volatility Duration Models," Working Papers 97-46, Centre de Recherche en Economie et Statistique.
  31. Carrasco, Marine & Chernov, Mikhail & Florens, Jean-Pierre & Ghysels, Eric, 2007. "Efficient estimation of general dynamic models with a continuum of moment conditions," Journal of Econometrics, Elsevier, vol. 140(2), pages 529-573, October.
  32. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
  33. Robert F. Engle, 1996. "The Econometrics of Ultra-High Frequency Data," NBER Working Papers 5816, National Bureau of Economic Research, Inc.
  34. Pham, Tuan D. & Tran, Lanh T., 1985. "Some mixing properties of time series models," Stochastic Processes and their Applications, Elsevier, vol. 19(2), pages 297-303, April.
  35. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Wiley Blackwell, vol. 61(2), pages 247-64, April.
  36. Shephard, Neil (ed.), 2005. "Stochastic Volatility: Selected Readings," OUP Catalogue, Oxford University Press, number 9780199257201.
  37. Asger Lunde & Peter Reinhard Hansen, 2001. "A Forecast Comparison of Volatility Models: Does Anything Beat a GARCH(1,1)?," Working Papers 2001-04, Brown University, Department of Economics.
  38. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July.
  39. Stanton, Richard, 1997. " A Nonparametric Model of Term Structure Dynamics and the Market Price of Interest Rate Risk," Journal of Finance, American Finance Association, vol. 52(5), pages 1973-2002, December.
  40. Fan J. & Zhang C., 2003. "A Reexamination of Diffusion Estimators With Applications to Financial Model Validation," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 118-134, January.
  41. Abadir, Karim M. & Lawford, Steve, 2004. "Optimal asymmetric kernels," Economics Letters, Elsevier, vol. 83(1), pages 61-68, April.
  42. Bouezmarni, Taoufik & Scaillet, Olivier, 2005. "Consistency Of Asymmetric Kernel Density Estimators And Smoothed Histograms With Application To Income Data," Econometric Theory, Cambridge University Press, vol. 21(02), pages 390-412, April.
  43. Fare, Rolf & Grosskopf, Shawna & Noh, Dong-Woon & Weber, William, 2005. "Characteristics of a polluting technology: theory and practice," Journal of Econometrics, Elsevier, vol. 126(2), pages 469-492, June.
  44. Oliver LINTON, . "Applied nonparametric methods," Statistic und Oekonometrie 9312, Humboldt Universitaet Berlin.
  45. Grammig, Joachim & Wellner, Marc, 2002. "Modeling the interdependence of volatility and inter-transaction duration processes," Journal of Econometrics, Elsevier, vol. 106(2), pages 369-400, February.
  46. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
  47. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
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Citations

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Cited by:
  1. Golyandina, Nina & Pepelyshev, Andrey & Steland, Ansgar, 2012. "New approaches to nonparametric density estimation and selection of smoothing parameters," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2206-2218.
  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. BOUEZMARNI, Taoufik & ROMBOUTS, Jeroen V.K., 2007. "Semiparametric multivariate density estimation for positive data using copulas," CORE Discussion Papers 2007054, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Taoufik Bouezmarni & Jeroen V.K. Rombouts, 2007. "Nonparametric density estimation for multivariate bounded data," Cahiers de recherche 07-10, HEC Montréal, Institut d'économie appliquée.
  5. Malec, Peter & Schienle, Melanie, 2014. "Nonparametric kernel density estimation near the boundary," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 57-76.
  6. Taoufik Bouezmarni & Jeroen V.K. Rombouts, 2006. "Density and Hazard Rate Estimation for Censored and ?-mixing Data Using Gamma Kernels," Cahiers de recherche 06-16, HEC Montréal, Institut d'économie appliquée.

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