Time series variables are often affected by single identifiable 'shocks', like elections, changes to a law, introduction of a competitor, start or finish of a war, a scandal, etc.
The modeling of the occurrence of a shock and its effects may need to take into account several elements:
When the shock may occur (this could be random);
Whether this changes the probability or impact of other possible shocks;
The effect of the shock: magnitude and duration
This section looks at an example: modeling deaths from disease X and the effect of introducing a cure.
People are dying from some health problem X at a current rate of 88/month, and the rate appears to be increasing by 1.3 deaths/month with each month. However, a cure for this problem appears to be close to being finished. Estimates are that the cure will be available between 20 and 50 months from now, but nobody can say that any duration is more likely than any other. Tests so far show that it is expected that there is only a 30% chance the cure will work for a treated person.
Forecast the number of deaths there will be for the next 100 months if the cure is approved and if not approved.
The models below offer a solution to this problem using different software: