The period column is in string format. can we change it to date. if we change it to date format your requirement is easy.
That's(Period) not a date format . Tableau will consider it like a string only.
Actually what i am pointing , Is the period is date or not? if it is a date field it need to be written in date format or else it will be problem.
At the moment its a String. But Its okey to convert it to a date format.
You this formula. formulate your period column into date filed then this will work.
YTD for previous year replace [Date] with your desired date, returns True if the date is in the YTD from the previous year
YEAR([Date]) == YEAR(TODAY())-1 AND (MONTH([Date]) < MONTH(TODAY()) OR (MONTH([Date]) == MONTH(TODAY()) AND DAY([Date]) <= DAY(TODAY())))