October 2022 Estimation of time series models using residuals dependence measures
Carlos Velasco
Author Affiliations +
Ann. Statist. 50(5): 3039-3063 (October 2022). DOI: 10.1214/22-AOS2220

Abstract

We propose new estimation methods for time series models, possibly noncausal and/or noninvertible, using serial dependence information from the characteristic function of model residuals. This allows to impose the i.i.d. or martingale difference assumptions on the model errors to identify the unknown location of the roots of the lag polynomials for ARMA models without resorting to higher order moments or distributional assumptions. We consider generalized spectral density and cumulative distribution functions to measure residuals dependence at an increasing number of lags under both assumptions and discuss robust inference to higher order dependence when only mean independence is imposed on model errors. We study the consistency and asymptotic distribution of parameter estimates and discuss efficiency when different restrictions on error dependence are used simultaneously, including serial uncorrelation. Optimal weighting of continuous moment conditions yields maximum likelihood efficiency under independence for unknown error distribution. We investigate numerical implementation and finite sample properties of the new classes of estimates.

Funding Statement

Financial support from Ministerio de Economía y Competitividad (Spain), grants ECO2017-86009-P and PID2020-114664GB-I00 is gratefully acknowledged.

Acknowledgments

The author would like to thank an Associate Editor and two referees for very helpful comments on earlier versions of the paper.

Citation

Download Citation

Carlos Velasco. "Estimation of time series models using residuals dependence measures." Ann. Statist. 50 (5) 3039 - 3063, October 2022. https://doi.org/10.1214/22-AOS2220

Information

Received: 1 January 2022; Revised: 1 July 2022; Published: October 2022
First available in Project Euclid: 27 October 2022

MathSciNet: MR4500633
zbMATH: 07628850
Digital Object Identifier: 10.1214/22-AOS2220

Subjects:
Primary: 62M10
Secondary: 62M15

Keywords: Characteristic function , generalized method of moments , generalized spectral density , martingale difference , noncausal processes , noninvertible processes

Rights: Copyright © 2022 Institute of Mathematical Statistics

Vol.50 • No. 5 • October 2022
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