On the estimation of the marginal density of a moving average process

The authors present a new convolution-type kernel estimator of the marginal density of an MA(1) process with general error distribution. They prove the rootn-consistency of the nonparametric estimator and give asymptotic expressions for the mean square and the integrated mean square error of some unobservable version of the estimator. An extension to MA(q) processes is presented in the case of the mean integrated square error. Finally, a simulation study shows the good practical behaviour of the estimator and the strong connection between the estimator and its unobservable version in terms of the choice of the bandwidth.