Rate of convergence of a convolution-type estimator of the marginal density of a MA(1) process

Ángeles Saavedra and Ricardo Cao

Stochastic Processes and their Applications, 1999, vol. 80, issue 2, 129-155

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.

Keywords: Kernel; estimator; Moving-average; process; Smoothing; parameter; Time; series (search for similar items in EconPapers)
Date: 1999
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Citations: View citations in EconPapers (5)

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