If a Budget Record was saved with the incorrect date range, we do not have an option to change the date. 

1.  Delete the Budget Record with the incorrect date and correct Scenario ID by selecting File> Delete.
2.  Create a new Budget with correct date range and same Scenario ID.

OR

If data has already been entered in to the incorrectly dated Budget record, we can copy the budget information into the newly created budget record before deleting the incorrect one. 

Note: If the two budget date ranges have any of the same periods, the same Scenario ID will not be able to be used.  You will have to use a different Scenario ID on the new Budget record and then you can copy and delete the incorrect budget.