Enhancing financial time series forecasting: a comparative study of discrete wavelet transform and LSTM models for selected global indices

This study explores the potential and challenges of using machine learning (ML) and deep learning (DL) models for predicting stock indices, emphasizing the need for comprehensive evaluations across different models and market conditions. The research introduces the innovative use of wavelet coefficients as explanatory variables in neural networks, highlighting their ability to detect sharp changes in price levels and improve prediction accuracy. Multiresolution Analysis: Performing MRA at different time scales provides a detailed and comprehensive analysis of financial time series, which is crucial for accurate predictions. We analyzed three stock indices—WIG, WIG20, and S&P 500—using data from stooq.pl, spanning 15 years from July 1, 2009, to June 30, 2024, resulting in 3753 daily observations for WIG and WIG20, and 3774 for the S&P 500. The focus was on the closing prices of these indices. Our methodology involves a comparative analysis of Long Short-Term Memory (LSTM) models utilizing Discrete Wavelet Transform (DWT) to extract wavelet coefficients as explanatory variables for neural networks. Additionally, the ARIMA model was employed for comparison. Our findings indicate that extracted wavelet coefficients can enhance LSTM neural network performance by reducing out-of-sample error. However, selecting appropriate wavelet types and neural network architecture is crucial, necessitating thorough model selection techniques.