Do I need a Calendar?

Anonymous 

You can resort to using a calendar table, but in my opiniion it would be overkill. 
In this instace I would create a "Period" table including your fiscal period and year columns, a newly created YearPeriod column (in both the period table and the data table) which is basically:

YearPeriod = table[year] * 100 + table[period]
and also include an index column in the period table. 
the period table should have unique values for the YearPeriod column, and you create a one-to-many relationship between the period table and your data table by linking the YearPeriod column. 
Time Intelligence won't work, but you can write the equivalent DAX with the period table as your filter table (the index column will make it easy to reference filter periods).

If you however want to use a calendar table, you will need to include a date field in your data table (for example, the first day of the month for each period) to be able to link to the calendar table via a relationship.