An Improved ARIMA Method Based on Functional Principal Component Analysis and Bidirectional Bootstrap and Its Application to Stock Price Forecasting

Abstract

This paper proposes an improved ARIMA method based on functional principal component analysis and bi-directional bootstrap. The proposed method does not require a smoothness assumption, uses intraday prices as auxiliary information and considers their functional characteristics, and effectively performs a bias-variance trade-off in the forecasting model by using a bi-directional bootstrap method. This is achieved by forming a paired sample of ARIMA forecast residuals and functional characteristics, and then fitting the forecast residuals to the regression model using the two-way bootstrap method, thereby improving the forecast accuracy.In addition, the choice of regression model is free. The empirical results show that the proposed method has better predictive performance and is more robust than the ARIMA model. Finally, the proposed method can be extended to environmental science, social science and other fields to help deal with various prediction problems.