A Time Series Data Regression Analysis based on B-spline Basis Expansion and Distance Covariance Weighted Stacking Framework

Abstract

Aiming at the problem of time series data regression prediction, this paper proposed a methodology for time series prediction based on data augmentation and cosine similarity weighted model average in the case where the predictor and response variable is a time series and the continuous scalar respectively. The constructed method deals with the problems of high dimension and noise of time series through B-spline basis expansion in which Blending algorithm was used to enhance the correlation information between B-spline basis coefficients and response variables, so as to further reduce the influence of noise on prediction models. Next, the cosine similarity model average is used to capture the unknown latent model structure between characteristic and response variables to improve the prediction accuracy of the model. The proposed method can effectively balance the bias and variance of the prediction model. In addition, the regression method in the technique is model-free. The analysis of actual data shows that the proposed method has certain advantages compared with those existing. Eventually, the method can be extended to forecasting applications in the fields of stock price prediction, social science, medicine and so on.