Abstract

This study conducts elaborate development and critique of the Exponentiated-Exponential Autoregressive Model (EEAR(p)). The formal model Equation has been defined theoretically, and the requirements for a unique nonzero fixed point are well established. In addition, a thorough stability condition was also specified. This criterion is based on analysing the roots of the characteristic Equation, the nonlinear transformation coefficients, and the h functions; in particular, the h functions require that all roots lie strictly within the unit circle. The analysis of the theoretical assumptions further confirmed that the EEAR model exhibits constant dynamics unless specific parameters for the combination of the linear and weighted exponential components are met. The EEAR model was empirically applied to weekly silver prices, with estimates up to the tenth order and evaluated using the information criteria (AIC, BIC, HQC, CAIC), along with a dynamic stability check via polynomial root analysis. Results showed that EEAR (5) was the most suitable specification, as it had the smallest AIC among stable models and the lowest residual variability. In addition, path diagrams show the practical application of EEAR stability (5), since the trajectory converges to a single consistent point, thereby significantly supporting predictability. These findings, combined with the findings presented, confirm that the EEAR (5) model has shown to be more flexible and better able to model the financial time series of interest, validating the effectiveness of a dynamic analysis in combination with statistical properties, to provide strong models to nonlinearity model formulation.