Gaussian process regression model based on stacking algorithm and application to stock price prediction

Gaussian process regression, as a nonparametric statistical method capable of fitting nonlinear functions, holds an important place in the realm of quantitative finance. However, when applied to the prediction of noisy stock price time series, a single Gaussian process regression is prone to overfitting, and its computational efficiency diminishes with an increase in data volume. Considering this, we propose an ensemble learning model for Gaussian processes based on Bootstrap and stacking algorithms. The proposed approach balances the training and testing errors of individual predictive models through the concept of model averaging. Additionally, it enhances the computational efficiency of Gaussian process regression by employing subsamples instead of the full sample. Furthermore, by utilizing the stacking model, it can surpass the predictive limits of Gaussian processes, thus enhancing the predictive performance of the method. Simulated data analysis indicates that under the assumption of a Gaussian process model, the proposed method exhibits smaller mean squared error, absolute error, and relative error compared to some classical methods. Ultimately, when applied to the task of predicting stock price movements, it demonstrates higher accuracy and stability.