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Time Series Nonparametric Regression Using Asymmetric Kernels with an Application to Estimation of Scalar Diffusion Processes

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  • Nikolay Gospodinov

    (Department of Economics, Concordia University and CIREQ)

  • Masayuki Hirukawa

    (Department of Economics, Northern Illinois University)

Abstract

This paper considers a nonstandard kernel regression for strongly mixing processes when the regressor is nonnegative. The nonparametric regression is implemented using asymmetric kernels [Gamma (Chen, 2000b), Inverse Gaussian and Reciprocal Inverse Gaussian (Scaillet, 2004) kernels] that possess some appealing properties such as lack of boundary bias and adaptability in the amount of smoothing. The paper investigates the asymptotic and finite-sample properties of the asymmetric kernel Nadaraya-Watson, local linear, and re-weighted Nadaraya-Watson estimators. Pointwise weak consistency, rates of convergence and asymptotic normality are established for each of these estimators. As an important economic application of asymmetric kernel regression estimators, we reexamine the problem of estimating scalar diffusion processes.

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Bibliographic Info

Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-573.

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Length: 63pages
Date of creation: Jun 2008
Date of revision:
Handle: RePEc:tky:fseres:2008cf573

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  1. Christopher S. Jones, 2003. "Nonlinear Mean Reversion in the Short-Term Interest Rate," Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 793-843, July.
  2. Lu, Zudi & Linton, Oliver, 2007. "Local Linear Fitting Under Near Epoch Dependence," Econometric Theory, Cambridge University Press, vol. 23(01), pages 37-70, February.
  3. 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.
  4. Chen, Song Xi, 1999. "Local linear smoothers using asymmetric kernels," SFB 373 Discussion Papers 1999,100, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  5. Fernandes, Marcelo & Monteiro, Paulo Klinger, 2004. "Central limit theorem for asymmetric kernel functionals," Economics Working Papers (Ensaios Economicos da EPGE) 522, FGV/EPGE Escola Brasileira de Economia e Finan├žas, Getulio Vargas Foundation (Brazil).
  6. Chen, Song Xi, 1999. "Beta kernel estimators for density functions," Computational Statistics & Data Analysis, Elsevier, vol. 31(2), pages 131-145, August.
  7. Matthias Hagmann & Olivier Scaillet, 2004. "Local Multiplicative Bias Correction For Asymmetric Kernel Density Estimators," Royal Economic Society Annual Conference 2004 25, Royal Economic Society.
  8. Jun Yu & Peter Phillips, 2004. "Jackknifing Bond Option Prices," Econometric Society 2004 North American Winter Meetings 115, Econometric Society.
  9. M.C. Jones & D.A. Henderson, 2007. "Miscellanea Kernel-Type Density Estimation on the Unit Interval," Biometrika, Biometrika Trust, vol. 94(4), pages 977-984.
  10. Peter Hall & Rodney C. L. Wolff & Qiwei Yao, 1999. "Methods for estimating a conditional distribution function," LSE Research Online Documents on Economics 6631, London School of Economics and Political Science, LSE Library.
  11. Bandi, Federico M., 2002. "Short-term interest rate dynamics: a spatial approach," Journal of Financial Economics, Elsevier, vol. 65(1), pages 73-110, July.
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