(untitled) (Contemporary Mathematics, 2024)
Fuzzy logic has been introduced as a modeler suitable for many situations where the data may be uncertain, and difficult to be described via the existing exact and analytic tools. However, although fuzzy models have succeeded to fit many situations, they fail in many others especially nonlinear, non-stationary, volatile, fuzzy, and fluctuated data such as financial time series. In this context, the need has emerged for more effective models to describe the data while preserving the fuzzy model as a basic descriptor of data fuzziness. In the present work, we develop a hybrid approach combining the Takagi-Sugeno fuzzy model with the wavelet decomposition to investigate financial time series as complex systems. The new approach showed effectively a high performance compared to existing methods via error estimates and Lyapunov theory of stability. The model is applied empirically to the Saudi Arabia Tadawul market traded over the period January 01, 2011, to December 31, 2022, a period characterized by many critical movements and phenomena such as the Arab Spring, Qatar embargo, Yemen war, NEOM project, 2030 KSA vision and the last COVID-19 pandemic, which makes its study of great importance to understand markets situations and also for policymakers, managers and investors.