## The Annals of Statistics

### Estimation of semivarying coefficient time series models with ARMA errors

#### Abstract

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

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

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

https://projecteuclid.org/euclid.aos/1467894710

Digital Object Identifier
doi:10.1214/15-AOS1430

Mathematical Reviews number (MathSciNet)
MR3519935

Zentralblatt MATH identifier
1346.60020

#### Citation

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. https://projecteuclid.org/euclid.aos/1467894710

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