High-Frequency Time Series Data Regression Based on the Functional Bayesian Model Averaging

Abstract

Regression analysis of high-frequency time series data has been an important problem in the field of statistical learning. In this paper, we propose a novel approach based on multiple basis function expansions and Bayesian model averaging when the predictor variable is a high-frequency time series and the response variable is continuous scalar data. On the one hand, the proposed method avoids the curse of dimensionality and extracts the functional information of the original sequence by transforming the discrete data into continuous functions in a function space consisting of some fixed basis functions. On the other hand, for the choice of basis functions, this paper proposes to adaptively determine the optimal solution using Bayesian model averaging, effectively balancing the variance and bias of the predictive model. The real data analysis shows that the proposed method has smaller mean squared error and absolute error, and is robust compared to other methods. Finally, the proposed method can be further extended to time series data applications such as weather forecasting and stock price prediction.