Cost forecasts are used to (an input for) monitor and control project work. (Monitoring and controlling the project work is one of the integration PMI processes.) The cost forecasts are calculated as estimate at completion (EAC) as part of the control costs PMI process.
Cost forecasts are described in sections 184.108.40.206 and 220.127.116.11 of the PMBOK, 5th edition.
Related: forecasting methods