QMLE for Periodic Time-Varying Asymmetric $$\log $$ GARCH Models

Analytical Study of Nonlinear Systems of Higher-Order Difference Equations: Solutions, Stability, and Numerical Simulations

“…In this subsection, we examine System (2), an extension of System (1). By examining the relationships within System (2), we deduce the following pattern:…”

“…In recent years, there has been a growing emphasis on exploring nonlinear systems of difference equations, driven by a quest for analytical solutions, deeper insights into dynamic behaviors, and applications spanning diverse disciplines including biology, physics, probability theory, environmental science, and engineering. These systems serve as discrete analogs to differential equations, offering a robust framework for modeling time-series data such as economic indicators (e.g., Gross Domestic Product, inflation rates, exchange rates) inherently measured at discrete intervals (see, [1,2]). Existing research has probed various facets of nonlinear dynamics, encompassing local dynamics, topological classifications, bifurcation analysis, and chaos control.…”