Nonparametric density estimation for linear processes with infinite variance |
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Authors: | Toshio Honda |
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Institution: | (1) Graduate School of Economics, Hitotsubashi University, 2-1 Naka, Kunitachi, Tokyo 186-8601, Japan |
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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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Keywords: | Linear processes Kernel density estimator Domain of attraction Stable distribution Noncentral limit theorem Martingale central limit theorem |
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