A Quantum-Enhanced Regime-Switching Model for Financial Time Series Forecasting

The ability to model and forecast financial time series is essential for modern economic strategy, guiding critical decisions in risk management, asset allocation, and derivative pricing. While traditional econometric models, such as Autoregressive Integrated Moving Average (ARIMA) and Generalized Autoregressive Conditional Heteroskedasticity (GARCH), perform well in stable conditions, they often fail to capture the abrupt regime shifts that characterise real-world markets. Detecting these structural breaks as they emerge, rather than a posteriori, remains a major challenge for effective forecasting. This thesis investigates how quantum mechanics can offer both a novel mathematical framework and a computational advantage to address this challenge. The financial market, with its vast number of interacting agents, inherent uncertainty, and rapid shifts in collective sentiment, provides a fertile domain for applying quantum-inspired methods. Where classical models struggle with structural non-linearities and high-dimensional data, quantum formalisms offer a new lens to model this complexity. Specifically, this research investigates two complementary quantum approaches. First, it explores the quantum probability formalism, wherein a Schrödinger-like trading equation gives rise to discrete energy levels in market dynamics, providing a theoretical basis for the multimodal distributions observed in asset returns. This approach offers a richer interpretation of market evolution by modelling phenomena such as the superposition of investor beliefs and interference effects. Second, this work provides experimental validation for the correspondence between these quantum-like states and financial market regimes by using a quantum two-sample test to detect structural breaks. By comparing return distributions from rolling time windows, this test identifies market transitions with greater sensitivity than classical methods, and its output is used to select between distinct econometric models (ARIMA-GARCH), which have been pre-calibrated on the uni-modal and multi-modal regimes, enhancing risk management.