The Annals of Statistics

Estimation of semivarying coefficient time series models with ARMA errors

Huang Lei, Yingcun Xia, and Xu Qin

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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.

Article information

Ann. Statist., Volume 44, Number 4 (2016), 1618-1660.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

ARMA process B-spline correlated errors semi-varying coefficient model spectral density function Whittle likelihood estimation


Lei, Huang; Xia, Yingcun; Qin, Xu. Estimation of semivarying coefficient time series models with ARMA errors. Ann. Statist. 44 (2016), no. 4, 1618--1660. doi:10.1214/15-AOS1430.

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