Forecasting S&P 500 Stock Prices using ARIMA Model Estimated by Particle Swarm Optimization Diagnosis

In recent years, neural networks have garnered significant attention in portfolio management, particularly for forecasting stock prices, which is a challenging yet crucial task for the financial market. This study focuses on the S&P 500, a benchmark index that comprises 500 major stocks and serves as a key indicator of the U.S. economy's health. For passive investors, the S&P 500 represents an essential exposure to the U.S. market through index funds. The research addresses the need for accurate stock price predictions by investigating the effectiveness of deep learning models in this domain. In this study, we introduce an innovative approach that combines Particle Swarm Optimization (PSO) with the Autoregressive Integrated Moving Average (ARIMA) model, creating a hybrid PSO-ARIMA framework designed to improve stock price forecasting accuracy. Through rigorous comparative analysis, the predictive capabilities of the PSO-ARIMA model are evaluated alongside popular models like GRU, LSTM, and traditional ARIMA. Results indicate that the PSO-ARIMA model outperforms these models across all evaluation metrics, including Mean Squared Error (MSE), achieving an MSE of 170.766, highlighting its superior precision and efficiency. The PSO-ARIMA model's effectiveness stems from its ability to leverage the strengths of both ARIMA and PSO-ARIMA models are well-suited for capturing linear trends in time series data, but they often struggle with complex, non-linear patterns common in stock price movements. By integrating PSO, a metaheuristic optimization technique, the model can optimize ARIMA's parameters to better fit the non-linear characteristics of financial data.