Estimation of population spectrum for linear processes with random coefficients

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.