Open Access
August 2016 Estimation of semivarying coefficient time series models with ARMA errors
Huang Lei, Yingcun Xia, Xu Qin
Ann. Statist. 44(4): 1618-1660 (August 2016). DOI: 10.1214/15-AOS1430


Serial correlation in the residuals of time series models can cause bias in both model estimation and prediction. However, models with such serially correlated residuals are difficult to estimate, especially when the regression function is nonlinear. Existing estimation methods require strong assumption for the relation between the residuals and the regressors, which excludes the commonly used autoregressive models in time series analysis. By extending the Whittle likelihood estimation, this paper investigates in details a semi-parametric autoregressive model with ARMA sequence of residuals. Asymptotic normality of the estimators is established, and a model selection procedure is proposed. Numerical examples are employed to illustrate the performance of the proposed estimation method and the necessity of incorporating the serial correlation in the residuals.


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Huang Lei. Yingcun Xia. Xu Qin. "Estimation of semivarying coefficient time series models with ARMA errors." Ann. Statist. 44 (4) 1618 - 1660, August 2016.


Received: 1 August 2015; Revised: 1 December 2015; Published: August 2016
First available in Project Euclid: 7 July 2016

zbMATH: 1346.60020
MathSciNet: MR3519935
Digital Object Identifier: 10.1214/15-AOS1430

Primary: 60K35

Keywords: ARMA process , B-spline , Correlated errors , semi-varying coefficient model , spectral density function , Whittle likelihood estimation

Rights: Copyright © 2016 Institute of Mathematical Statistics

Vol.44 • No. 4 • August 2016
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