Stochastic analysis of COVID19 impact on birth life expectation

This framework consists in an application of an ARIMA model in order to analyze the impact of COVID19 pandemic on the birth life expectation process with a Impulse Response Function. More precisely 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 birth life expectation in a deterministic trend component and a residual part where we will model with an ARIMA model with order 2 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 the one with shock. Then, we complete the comparison looking at the observed birth life expectation in order to see if the realty is following the theoretical framework.