Double smoothing local linear estimation in nonlinear time series

Abstract

We generalize the double smoothing local linear regression method to nonparametric regression of time series. Under a strong mixing condition for the dependence of the time series, we show that after another round of smoothing based on the local linear regression estimates, the double smoothing local linear estimate will have reduced asymptotic bias, while keeping the variance at the same asymptotic order. The asymptotic bias reduces from the order of h² for the local linear estimates to h⁴ for the double smoothing local linear estimates, where h is the bandwidth. Hence the double smoothing local linear method produces more optimal estimates in terms of mean squared error. Simulation studies and real time series data analysis confirm the advantages of the double smoothing method compared to the local linear method.

Keywords:

• Non parametric regression
• local linear regression
• double smoothing local linear regression
• time series
• asymptotic properties

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (No.11471252) and Fundamental Research Funds for Central Universities (No. CCNU18ZDPY08).