Statistics and Its Interface

Volume 10 (2017)

Number 1

Detecting hidden periodicities for models with cyclical errors

Pages: 107 – 118



María Pilar Frías (Department of Statistics and Operations Research, University of Jaén, Spain)

Alexander V. Ivanov (National Technical University, Kyiv Polytechnic Institute, Ukraine)

Nikolai Leonenko (School of Mathematics, Cardiff University, Cardiff, Wales, United Kingdom)

Francisco Martínez (Department of Computer Science, University of Jaén, Spain)

María Dolores Ruiz-Medina (Department of Statistics and Operations Research, University of Granada, Spain)


In this paper, the estimation of parameters in the harmonic regression with cyclically dependent errors is addressed. Asymptotic properties of the least-squares estimates are analyzed by simulation experiments. By numerical simulation, we prove that consistency and asymptotic normality of the least-squares parameter estimator studied holds under different scenarios, where theoretical results do not exist, and have yet to be proven. In particular, these two asymptotic properties are shown by simulations for the least-squares parameter estimator in the non-linear regression model analyzed, when its error term is defined as a non-linear transformation of a Gaussian random process displaying long-range dependence.


asymptotic distribution theory, asymptotic inference, hidden periodicities, nonlinear regression, vector parameter

2010 Mathematics Subject Classification

Primary 62E20. Secondary 60G18, 62F10.

Published 27 September 2016