In this paper, we study the spectral density estimation of an almost periodically correlated continuous-time random process using Poisson sampling. Under certain regularity conditions on the weak dependence of such a process, we give an estimator of its spectral density and establish the root-mean-square consistency and the asymptotic normality of this one. Finally, we completed the theoretical study with simulation work.

root-mean-square consistency, asymptotic normality, spectral densities, estimation, Poissonian sampling, weakly dependent process, almost-periodic process, almost-periodically correlated processes.

Received: December 17, 2020; Accepted: January 21, 2021; Published: March 18, 2021

How to cite this article: Sylvestre Placide Ekra and Vincent Monsan, Asymptotic property of spectral density estimators of a continuous time process almost periodically correlated low dependent by Poisson, Far East Journal of Theoretical Statistics 61(2) (2021), 145-189. DOI: 10.17654/TS061020145

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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