A Study on Global Cyclicality of the S&P 500 Index Using a Hybrid Model of Recurrent Neural Networks and Fourier Transformations

The S&P 500 index is one of the most important and widely followed indices in capital markets. It serves as an indicator of the state of the U.S. economy, making it a compelling subject of study. This article presents a study on the existence of global cyclicality in the dynamics of the S&P 500 index. For this purpose, a hybrid analytical approach has been applied, combining Long Short-Term Memory (LSTM) neural networks with spectral analysis using Fourier transformations. The conducted experiments identified a Recurrent Neural Network (RNN) that accurately approximates the index’s movement over the period from 2014 to 2024. However, no global cyclicality was found in the S&P 500 data, indicating that the index’s movements are predominantly chaotic and nonlinear, without stable and recurring global patterns. Short-term cyclicality with a period of 80–90 days was identified.