The consistency of model selection for dynamic Semi-varying coefficient models with autocorrelated errors

ABSTRACT

The consistency of model selection criterion BIC has been well and widely studied for many nonlinear regression models. However, few of them had considered models with lag variables as regressors and auto-correlated errors in time series settings, which is common in both linear and nonlinear time series modeling. This paper studies a dynamic semi-varying coefficient model with ARMA errors, using an approach based on spectrum analysis of time series. The consistency property of the proposed model selection criteria is established and an implementation procedure of model selection is proposed for practitioners. Simulation studies have also been conducted to numerically show the consistency property.

Keywords:

• ARMA errors
• BIC
• Lag variable
• Spectral density function
• Whittle likelihood

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G05
• 62M10

Acknowledgements

The authors would like to thank the Editors and three referees for detailed and insightful comments, by which a substantial improvement of this paper could be made. The authors acknowledge supports from the National Natural Science Foundation of China 11601447; the Fundamental Research Funds for the Central Universities 2682016CX107 and 2682017RSC33; the China Scholarship Council 201707005036.