Is the Brownian bridge a good noise model on the boundary of a circle?

Giacomo Aletti () and Matteo Ruffini ()
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Giacomo Aletti: Università degli Studi di Milano
Matteo Ruffini: C/Diputacin, 303, Ático

Annals of the Institute of Statistical Mathematics, 2017, vol. 69, issue 2, No 6, 389-416

Abstract: Abstract In this paper, we study periodical stochastic processes, and we define the conditions that are needed by a model to be a good noise model on the circumference. The classes of processes that fit the required conditions are studied together with their expansion in random Fourier series to provide results about their path regularity. Finally, we discuss a simple and flexible parametric model with prescribed regularity that is used in applications, and we prove the asymptotic properties of the maximum likelihood estimates of model parameters.

Keywords: Fourier transform; Karhunen–Loève’s theorem; Gaussian processes; Periodic processes; Stationary processes; Maximum likelihood (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10463-015-0546-5

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