Research And Applications Of Several Nonparametric Methods In Nonlinear Time Series Analysis

In traditional parametric regression models,the functional form of the model is specified before the model is fit to dataand the object is to estimate the parameters of the model.In nonparametric regression,in contrast,the object is to estimate the regression function directly without specifying its form explicitly.Here we describe how to fit several kinds of nonparametric regression models.There are many kinds of nonparametric regression methods such as the kernel smoothing,local linear regression,double smoothing local linear regression,alterna-tive conditional estimation method,penalized regression method,wavelet method,smoothing spline method,orthogonal regression and so on.Local linear regression method is widely used because this method is simple and convenient,but it has a larger variance.Although the asymptotic properties of local linear method is good,but the error is large for sparse data,so will not be commonly used.Therefore,people made a further improvement in the local linear regression method,after two steps of smoothing,called double smoothing local linear regression method.In the condition of independent data,the improved method will reduce the order of the asymptotic bias.In practice,the data may be correlated,such as time series.Statistically,time series analysis has a strong applicability and is widely used in real life with ap-plication in many fields,such as economics,finance,weather forecast,mechanical,chemical industry and so on.There are more research on linear time series,but the actual data is often nonlinear.Some scholars have started to analyze nonlinear time series data using nonparametric regression methods such as local linear regression.This research focuses on applying nonparametric regression methods in non-linear time series data.First,two simulated data sets were generated using Self-Exciting Threshold Autoregressive(SETAR)models and Additive Autoregressive (AAR)models.Among nonparametric regression methods,alternative conditional estimation method,penalized regression method and local linear regression method have been applied for the simulated nonlinear time series data.The application of double smoothing local linear regression method in the analysis of nonlinear time series was introduced as a new nonparametric regres-sion method.For dependent data,after two step of smoothing,estimates with reduced asymptotic bias,from h2 to h4,while keeping the asymptotic variance at the same order,which is more optimized than the local linear regression method was obtained.A simulated time series data set was used to show the performances of double smoothing local linear regression method with local linear regression method.Nonparametric methods,alternating condition expectation algorithm,penalize cubic regression,local linear and double smoothing local linear regression methods were applied in four rea.l data sets(BOVESPA index,SENSEX index,FTSE index and S&P S120 index).Models fitted using most popular parametric method Box-Jenkins and models fitted using nonparametric regression methods were compared using the error measure root mean square error.Though double smoothing local linear regression method perform better than local linear regression method for al-1 real time series data sets,except for the BOVESPA index data set,alternating conditional expectation algorithm was perform better than double smoothing local linear method.Finally,alternating conditional expectation algorithm was selected as the most suitable method to model S$P SL20 index in Colombo Stock Exchange,Sri Lanka.