What is the nature of life expectation’s time series?

We aim to determine the optimal approach for characterizing the nature of a process: life expectancy at birth. We will explore various specifications to identify the most suitable one for describing its inherent characteristics. The paper demonstrates that the primary component of the process is the trend, and it is reasonable to assume that the residuals’ values in each year depend on the occurrences of the preceding year. Consequently, we conclude that the most effective model for capturing the stochastic process of life expectancy at birth is an ARIMAX (1,1,1) with the trend serving as the explanatory variable.