Limit-Cycle Behavior of the Exponentiated Exponential Autoregressive Model: Theory and Applications

This study aims to design and evaluate a special nonlinear time series model, namely the exponentiated exponential autoregressive (EEAR) model, used to construct time series estimates that incorporate the cumulative distribution function of the raised exponential distribution. The underlying analytical constraints on the stability of these models and their limit cycles were obtained via local linearization techniques. The resulting models were developed by applying them to real data (monthly average of British pounds (in millions) spent by foreign visitors in the United Kingdom for the period 1-1-1988 to 31-12-2018) and indicated how efficiently they can capture the intricate dynamic character of data. The EEAR model was the best model according to information criteria, fit quality, and dynamically stable with respect to the different types of ordered models. The study represents a substantial improvement to the nonlinear time series model's theory, as well as new analytical resources to model complex economic and financial phenomena.