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Nonparametric Density Estimation for Linear Processes with Infinite Variance

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  • Honda, Toshio
  • 本田, 敏雄

Abstract

We consider nonparametric estimation of marginal density functions of linear processes by using kernel density estimators. We assume that the innovation processes are i.i.d. and have infinite-variance. We present the asymptotic distributions of the kernel density estimators with the order of bandwidths fixed as h=cn-1/5, where n is the sample size. The asymptotic distributions depend on both the coefficients of linear processes and the tail behavior of the innovations. In some cases, the kernel estimators have the same asymptotic distributions as for i.i.d. observations. In other cases, the normalized kernel density estimators converge in distribution to stable distributions. A simulation study is also carried out to examine small sample properties.
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Suggested Citation

  • Honda, Toshio & 本田, 敏雄, 2006. "Nonparametric Density Estimation for Linear Processes with Infinite Variance," Discussion Papers 2005-13, Graduate School of Economics, Hitotsubashi University.
    • Handle: RePEc:hit:econdp:2005-13
    Note: February 2006; August 2006 (Revised)
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    Cited by:

    1. Toshio Honda, 2010. "Nonparametric estimation of conditional medians for linear and related processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(6), pages 995-1021, December.
    2. Toshio Honda, 2013. "Nonparametric quantile regression with heavy-tailed and strongly dependent errors," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(1), pages 23-47, February.
    3. Chang, Yoosoon & Kim, Chang Sik & Park, Joon Y., 2016. "Nonstationarity in time series of state densities," Journal of Econometrics, Elsevier, vol. 192(1), pages 152-167.

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