Stock Price Forecasting Through Symbolic Dynamics and State Transition Graphs With a Convolutional Recurrent Neural Network Architecture

Abstract

Accurate stock price forecasting remains a critical challenge in financial analytics due to volatile market conditions, non-stationary dynamics, and abrupt regime shifts that often defy traditional modeling techniques. This study proposes a comprehensive framework for stock price forecasting that integrates symbolic dynamics, graph-based state representations, and deep learning. By converting continuous-valued stock prices into discrete symbolic states representing amplitude and trend information, the method constructs transition matrices capturing probabilistic relationships within financial time series. These transition matrices are then processed by a convolutional recurrent neural network (CRNN), in which convolutional layers isolate local spatial dependencies in the symbolic-state domain, while recurrent LSTM layers capture multi-scale temporal dynamics extending across multiple time horizons. Experimental evaluations are conducted over prediction horizons of 1 day, 10 days, and 100 days, spanning pre-COVID, COVID, and post-COVID market regimes. The results indicate that while longer prediction horizons naturally incur greater forecasting uncertainty due to compounding variability, the integration of symbolic-state preprocessing with deep temporal modeling demonstrates significant robustness in handling non-stationary financial environments. During the stable pre-COVID period, the proposed methodology achieves reductions in mean squared error (MSE) of up to 98% relative to the volatile COVID phase, highlighting its capability to effectively leverage well-defined market patterns in stable economic conditions. Furthermore, the model consistently delivers competitive forecasting performance across all prediction horizons and market regimes. Collectively, these findings emphasize the potential of symbolic-state-based deep learning architectures as a viable pathway to address the complexity and volatility characteristic of modern financial markets. © The Author(s) 2025.