The Application Of Regularized Least-Squares Regression To Time Series Model Based On Statistical Learning Theory

In the development of time series model, two stages are included: linear model and nonlinear model. Nonlinear time series model can be classificed into parameter models and nonparemeter models. With the development of Artifical Intelligence (AI), Neural Network (NN) and Support Vector Regression (SVR) are adopted into the time series forecasting model.Regularized Least-Squares Regression (RLSR) is a method of function estimation based on Statistical Learning (SL) theory. In this paper, we borrow the idea from using Neural Network (NN) and Support Vector Regession (SVR), and adopt the RLS method to the time series forecasting. After simuliating the RLS method with both stationary series and nonstationary series(with trend and seasonality), and get good performance. RLS method is applied to sunspot number, crude oil price, and GBP/USD currecy exchange rate times series forecasting. And the forecasting performance is better than the literature as far as we know. In addition, RLSR takes full use of the propertities of Reproducing Kernel Hilbert Space (RKHS), and the solution of RLSR is converted to solve a linear equation, the algorithm of RLS is comparably easier to be solved.The contributions of this paper are:●Adopt the Regularized Least-Squares Regression (RLSR) to the time series forecasting model.●Simulate the forecasting performance of RLS mothod with both stationary series and nonstationary series (with trend and seasonality).●Apply the RLS method to the sunspot number prediction.●Apply the RLS method to the crude oil price forecasting.●Apply the RLS method to the GBP/USD exchange rate (daily, weekly, and biweekly) forecasting.In the first chapter, this paper reviews the development of time series model, and introduces the forecasting evaluation and accuracy measures. In the second chapter, this paper introduces the RLSR theory based on Statistical Learning (SL) theory and gives the frame work on how to apply RLS and WRLS methods to time series forecasting.In the third chapter, this paper simulates the forecasting performance of RLS method with both stationary series and nonstationary series(with trend and seasonality). Parameters selection is detailed discussed.In the fourth chapter, RLS and WRLS methods are applied to forecast the sunspot numer. The performance of RLS method is comparable to the model in the latest literature as far as sunspot number is concerned, in addition that the algorithm of RLS method is much ealier to be solved.In the fifth chapter, RLS and WRLS methods are applied to forecast the crude oil price. The performance of RLS method is better than the models in the latest literature using the criteria of RMSE.In the sixth chapter, RLS and WRLS methods are applied to forecast GBP/USD currency exchange rate. The performance of RLS method is better than the currency exchange rate forecasting model in the latest literature as far as daiy and weekly GBP/USD exchange rate is concered.In the last chapter, this paper summarizes the result and gives some open problems needed to do further research.