Stock Prediction Model Based on Mixed Fractional Brownian Motion and Improved Fractional-Order Particle Swarm Optimization Algorithm

Abstract

As one of the main areas of value investing, the stock market attracts the attention of many investors. Among investors, market index movements are a focus of attention. In this paper, combining the efficient market hypothesis and the fractal market hypothesis, a stock prediction model based on mixed fractional Brownian motion (MFBM) and an improved fractional-order particle swarm optimization algorithm is proposed. First, the MFBM model is constructed by adjusting the parameters to mix geometric Brownian motion (GBM) and geometric fractional Brownian motion (GFBM). After that, an improved fractional-order particle swarm optimization algorithm is proposed. The position and velocity formulas of the fractional-order particle swarm optimization algorithm are improved using new fractional-order update formulas. The inertia weight in the update formula is set to be linearly decreasing. The improved fractional-order particle swarm optimization algorithm is used to optimize the coefficients of the MFBM model. Through experiments, the accuracy and validity of the prediction model are proven by combining the error analysis. The model with the improved fractional-order particle swarm optimization algorithm and MFBM is superior to GBM, GFBM, and MFBM models in stock price prediction.