The Application Of Double Smoothing Local Linear Regression In The Analysis Of Nonlinear Time Series

In statistics, the application of time series analysis is very strong, in real life more and more widely used in many fields, such as economics, finance, weather forecast, mechanical, chemical industry and so on. There are more research in linear time series, but the actual data is often nonlinear, some scholars have studied the application of local linear regression method in the analysis of nonlinear time series.There are many non-parametric regression methods, such as the local regression,wavelet method, smoothing spline method,orthogonal regression. Local linear regression is application more in local regression, because this method is simple and convenient, but it has larger variance. Therefore, people made a further improvement in the local linear regression method, after two steps of smoothing, called double smoothing local linear regression method. Although the asymptotic properties of local cubic is good, but the error is large for sparse data, so will not be commonly used. In the condition of independent data, the improved method will reduce the order of the asymptotic bias, but actually the data are related, such as time series.This paper focuses on the application of double smoothing local linear regression method in analysis of nonlinear time series. Asymptotic variance through two steps of smoothing keep the same order while reduce the order of the asymptotic bias, from h2 reduced to h4, more optimized than the local linear regression method.