Improved Density Estimators for Invertible Linear Processes

Anton Schick and Wolfgang Wefelmeyer

Communications in Statistics - Theory and Methods, 2009, vol. 38, issue 16-17, 3123-3147

Abstract: The stationary density of a centered invertible linear process 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 holds 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.

Date: 2009
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DOI: 10.1080/03610920902947592

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