A time series data regression based on a B-spline and stacking framework

Abstract This paper proposes a new time series regression method based on the combination of B-spline basis expansion and distance covariance weighted model. This paper considers the case that the predictor variable is a time series and the response variable is a continuous scalar. In order to solve these problems of high dimension and high noise of time series, this proposed method uses a B-spline basis to reduce the dimension and extract the function information of the original sequence. Considering that there is still some noise in the reduced dimension random variables, this proposed method considers using the stacking framework to enhance the data. Since the importance of each basis model is unknown, this paper uses the distance covariance to measure the importance of the basis model and develop a weighted stacking framework, which can adaptively weigh the bias and variance of the predictor model. In addition, each basis estimator in ensemble learning is model-free. The real data analysis shows that the proposed method is competitive with some existing methods. Finally, the proposed method can be directly applied to other fields such as environmental science, medical science and speech recognition et al.