I submitted your data to my visual automatic intervention detection procedure ( my trained eye ) , it identified a possible downwards trend for periods 1-100 and then upwards trend from 100-250 and three level shifts (intercept shift ) at 260 , 340 and 420. If I had your data I would submit it to AUTOBOX a commercially available package that I have helped to develop to confirm or correct my (probably flawed) first impression.
In all seriousness what you are after is an approach ( developed software ) that simultaneously deals with detecting and incorporating arima , level shifts , local time trends , seasonal pulses and pulses while adjusting for time varying parameters and tine varying error variance.
The problem/opportunity is to simultaneously identify BOTH arima structure & the Interventions.
Here is an interesting example