Deep Learning and Evolutionary Optimization for Financial Forecasting with Echo State Networks

Financial time series are inherently noisy, nonlinear, and non-stationary, shaped by a wide range of economic and societal factors, which makes accurate forecasting exceptionally challenging. Traditional statistical approaches, relying on econometric assumptions, often struggle to capture these complex dynamics. In contrast, Deep Learning (DL) methods, particularly recurrent architectures, have demonstrated superior predictive power. However, these models face challenges such as high training complexity and vanishing/exploding gradients. Echo State Networks (ESNs), a more recent recurrent paradigm, address many of these issues through a lightweight and computationally efficient design, showing promising results in financial forecasting. This thesis advances the application of ESNs for financial time series forecasting by focusing on their reservoir, the core element projecting inputs into a high dimensional dynamic state space. The reservoir is inherently black-box and susceptible to chaotic dynamics, which, if not properly managed, can undermine stability and predictive accuracy. To improve ESN performance, this research develops a principled optimization strategy that accounts for these dynamics. Specifically, a novel hybrid metaheuristic, the Self-Adaptive Cuckoo Genetic Algorithm (SACGA), is proposed. SACGA combines genetic algorithms with adaptive mutation and Lévy flight mechanisms, enabling efficient exploration of the ESN hyperparameter space while balancing forecasting accuracy with reservoir stability. A major contribution of this work is a systematic review of 187 Scopus-indexed studies (2020–2024) on DL applications in financial forecasting. The review categorizes approaches across domains, compares key architectures, and highlights persistent challenges, providing a consolidated knowledge base for researchers and practitioners. Extensive experiments on both synthetic chaotic benchmarks and real-world financial datasets demonstrate that SACGA-optimized ESNs consistently outperform standard models, exhibiting improved stability and interpretability. Chaos and dynamical-system-inspired diagnostics, including Lyapunov exponents, input separability, and kernel PCA projections, show that optimized reservoirs form well defined, low-dimensional structures, reflecting stable, organized internal dynamics with good generalizability. In contrast, random (unoptimized) reservoirs display scattered, disordered patterns (blobs), with unstable behavior. These findings support the central hypothesis of the thesis: that harnessing, rather than overlooking or mitigating intrinsic reservoir chaos can improve forecasting performance. Overall, this thesis contributes (i) a comprehensive review of deep learning in financial forecasting, (ii) a chaos-informed perspective on ESN reservoirs, (iii) the development of SACGA as a novel hybrid optimization algorithm tailored to ESNs, and (iv) diagnostic tools for reservoir analysis. Together, these contributions advance both the theoretical understanding and the practical application of ESNs in financial prediction.