An improved ARIMA model based on regularized Gaussian basis function and its application to stock price forecasting

Abstract

We propose an improved ARIMA model based on regularized Gaussian basis expansion, which is a generalized linear model. This approach takes into account the auxiliary information of intra-day prices, does not require the assumption of linear smoothing and is able to capture the functional features in high-dimensional time series. Specifically, the discrete series of intra-day prices are first functionalized by Gaussian basis smoothing and fitted to the residuals obtained from the ARIMA model using the basis function coefficients, and the fitted model is chosen as a random forest. The empirical results show that the RT-ARIMA model considering auxiliary information is more accurate than the original ARIMA model. And we performed a robustness test by adjusting the size of the training set, and the results show that the method is robust. This model is helpful to improve the accuracy of stock price prediction and other complicated stochastic systems.