Detecting hidden periodicities for models with cyclical errors

TL;DR

This paper investigates the estimation of parameters in harmonic regression models with cyclically dependent errors, demonstrating through simulations that least-squares estimators are consistent and asymptotically normal even in complex scenarios.

Contribution

It provides novel simulation evidence for the asymptotic properties of least-squares estimators in models with long-range dependent, non-linear error processes where theoretical proofs are lacking.

Findings

Consistency of least-squares estimators confirmed via simulations

Asymptotic normality demonstrated in complex error scenarios

Estimates hold in non-linear transformations of Gaussian processes

Abstract

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.