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Improved Density Estimators for Invertible Linear Processes

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  • Anton Schick
  • Wolfgang Wefelmeyer

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.

Suggested Citation

  • Anton Schick & Wolfgang Wefelmeyer, 2009. "Improved Density Estimators for Invertible Linear Processes," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 38(16-17), pages 3123-3147, October.
    • Handle: RePEc:taf:lstaxx:v:38:y:2009:i:16-17:p:3123-3147
    DOI: 10.1080/03610920902947592
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