Rate of convergence of a convolution-type estimator of the marginal density of a MA(1) process |
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Authors: | ngeles Saavedra,Ricardo Cao |
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Affiliation: | a Department of Statistics and Operations Research, University of Vigo, Spain;b Department of Mathematics, University of La Coruña, Spain |
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Abstract: | In this paper moving-average processes with no parametric assumption on the error distribution are considered. A new convolution-type estimator of the marginal density of a MA(1) is presented. This estimator is closely related to some previous ones used to estimate the integrated squared density and has a structure similar to the ordinary kernel density estimator. For second-order kernels, the rate of convergence of this new estimator is investigated and the rate of the optimal bandwidth obtained. Under limit conditions on the smoothing parameter the convolution-type estimator is proved to be -consistent, which contrasts with the asymptotic behavior of the ordinary kernel density estimator, that is only -consistent. |
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Keywords: | Kernel estimator Moving-average process Smoothing parameter Time series |
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