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Estimation of population spectrum for linear processes with random coefficients

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Abstract

A set of time series generated by stationary linear processes with an absolutely continuous spectral distribution is analysed. The time series can then be considered realizations of a linear process of random coefficients. Likewise, each spectral density function is a realization of a stochastic process whose function of means is called a population spectrum. We propose a kernel estimator for the population spectrum and give conditions for its consistency. We then illustrate the properties of this estimator in a simulation study and compare its performance with an alternative parametric estimator that can be found in the literature.

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Authors and Affiliations

  1. Department of Mathematics, University of Las Palmas de Gran Canaria, 35017, Las Palmas de Gran Canaria, Canary Islands, Spain

    P. Saavedra, C. N. Hernández, I. Luengo, J. Artiles & A. Santana

Authors
  1. P. Saavedra
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  2. C. N. Hernández
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  3. I. Luengo
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  4. J. Artiles
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  5. A. Santana
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Correspondence to P. Saavedra.

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Saavedra, P., Hernández, C.N., Luengo, I. et al. Estimation of population spectrum for linear processes with random coefficients. Computational Statistics 23, 79–98 (2008). https://doi.org/10.1007/s00180-007-0069-5

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  • DOI: https://doi.org/10.1007/s00180-007-0069-5

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