Forecasting Stock Market Trends of S&P 500 based on Fractal Theory and Polynomial Regression Model

Baozhen Che

doi:10.54097/vkc85b18

Authors

Baozhen Che

DOI:

https://doi.org/10.54097/vkc85b18

Keywords:

S&P 500, fractal theory, box dimension, polynomial regression model, forecast.

Abstract

The stock market is a key component of the national economy in the financial sector. Stock market analysis and prediction have consistently remained popular research directions, offering vital practical guidance for financial investments. Consequently, scholars from both domestic and international spheres have employed various methodologies to analyze and forecast stock market trends. This paper focuses on the Standard & Poor's 500 Index (S&P 500) as the primary research subject. By computing its box dimension, the paper provides insights into the future trends and complexities of the stock market using fractal theory and a polynomial regression model. Additionally, the paper presents trend-tracking strategies accordingly, offering valuable guidance to investors. The primary dataset used for this study is sourced from the Kaggle database, specifically comprising the closure prices for the S&P 500 Index ranging from September 3, 2013, to August 31, 2023. The results demonstrate the efficacy and validity of the proposed third-order polynomial regression model, with a root mean square error (RMSE) of 0.08. Moreover, a trading strategy that suggests appropriate buy or sell operations when the price trend coincides with the downward pattern of the box dimension is introduced. These findings provide theoretical and empirical references for the field of financial investment. However, it is essential to note that in order to enhance the predictive performance, future initiatives should incorporate a more extensive sample size and complement the polynomial regression model with combinations of other models.

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