Double smoothing local linear estimation in nonlinear time series

K. D. Prasangika, Wan Tang, Zeng Yao and Guoxin Zuo

Communications in Statistics - Theory and Methods, 2023, vol. 52, issue 5, 1385-1399

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.

Date: 2023
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DOI: 10.1080/03610926.2021.1927096

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