A novel partial-linear single-index model for time series data

Abstract

Partial-linear single-index models have been widely studied and applied, but their current applications to time series modeling still need some strong and inappropriate assumptions. A novel method which relaxes those assumptions is proposed. It extends the applicability of partial-linear single-index models to time series modeling, taking both lag variables and autocorrelated errors into consideration. An estimation procedure based on Whittle likelihood is proposed and some asymptotical properties of the corresponding estimators are derived. In addition, some simulation studies are conducted to elaborate that the proposed model is necessary in certain situations. The proposed models are also shown to be useful and reasonable in real data analysis, indicating the feasibility and practicability of the proposed estimation method.