## Estimation of semivarying coefficient time series models with ARMA errors.(English)Zbl 1346.60020

Summary: 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 assumptions 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 detail a semi-parametric autoregressive model with an 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.

### MSC:

 60F05 Central limit and other weak theorems 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62G05 Nonparametric estimation 62G08 Nonparametric regression and quantile regression 62G20 Asymptotic properties of nonparametric inference 65C60 Computational problems in statistics (MSC2010)
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