likelihood for dependent data; empirical likelihood with infinitely many constraints; infinite-order moving average process; infinite-order autoregressive process. ABSTRACT The stationary density of a centered invertible linear processes can be represented as a convolution of innovation-based densities, and it can be estimated at the parametric rate by plugging residual-based kernel estimators into the convolution representation. We have shown elsewhere that a functional central limit theorem

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... lds both in the space of continuous functions vanishing at infinity, and in weighted L 1 -spaces. Here we show that we can improve the plug-in estimator considerably, exploiting the information that the innovations are centered, and replacing the kernel estimators by weighted versions, using the empirical likelihood approach.