Payroll Period can be managed by the Admin through the 'Manage Payroll Period' under Payroll module

Payroll->Settings->Manage Payroll Period

New Payroll period can be created by entering the payroll period code, the From date will be next day of the last payroll period end date by default and it can not be modified, payroll to date and cutoff date can be entered and saved. 

Existing payroll period can be edited by clicking the edit icon from the grid.

Click below link to view create Manage Payroll Period Video: