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Nonparametric Density Estimation for Linear Processes with Infinite Variance

By Toshio Honda and 敏雄 本田


February 2006; August 2006 (Revised)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.[Revised version]34, [3] p

Topics: linear processes, kernel density estimator, domain of attraction, stable distribution, noncentral limit theorem, martingale central limit theorem
Publisher: Graduate School of Economics, Hitotsubashi University
Year: 2006
OAI identifier:
Provided by: HERMES-IR

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