Evaluating hybrid quantum–classical learning for financial forecasting: a comparative study with classical machine learning models on BSE indices

The forecasting of financial time series has gained more significance in decision making within a dynamic economic setting. Over the last few years, there has been a push in exploring both classical machine learning methods and novel quantum machine learning models with a view to enhance predictive accuracy. This paper suggests a quantum-classical regression framework developed that combines the feature selection in the form of a Random Forest in a hybrid approach, dimensionality reduction in the mode of Principal Component Analysis (PCA), and predicting in the form of a Variational Quantum Circuit (VQC). It is tested in various financial indicators, as BSE ESG, Carbon Exchange, Energy, Green Exchange, Oil and Gas and Power, with the help of RMSE and R 2 as the measure of performance. As experimental findings indicate, the classical algorithms like Random Forest and k-Nearest Neighbors always have the best accuracy and stability compared to quantum and hybrid ones. Quantum models are unstable, in contrast to Quantum kNN which is fairly stable. The hybrid model performs moderately with consistent error values but fairly lower explanatory power with significant results mostly on the BSE ESG data. In general, the paper has pointed out that classical approaches are still best in structured financial prediction tasks and hybrid quantum-classical models are potentially effective, but not yet competent. The results give valuable information on the existing limitation and future of the quantum machine learning to financial forecasting applications.