Investigation on life expectation at birth process nature.

This framework consists in an application of an ARIMAX model in order to analyze the impact of COVID19 pandemic on the life expectancy Malia (2021) at birth process with a Impulse Response Function. More pre- cisely we model the process, then we emulate the shock observed on this process to check if it is stable and trend reverting. In this way we decompose the time series of the life expectancy at birth in a deterministic trend compo- nent and a residual part where we will model with an ARIMAX model with order 1 in auto-regressive component and with order 1 for the integration component. We will show that residual could be considered as white noise and, then, that the process is estimated to be stable and trend reverting in few years. Finally we compare forecast of the model without shock with the one with shock. Then, we complete the comparison looking at the observed life expectancy at birth in order to see if the realty is following the theoretical framework.