To account for accrual balance, Purchasing period end activity requires that Payables period must be closed. This is to ensure that all invoice activities belonging in the period are finalized to have correct receipt accrual result. In fact, one cannot call the Receipt Acrual - Period End concurrent process in Purchasing for a period unless Payables has been closed for that period.
Inventory and Purchasing period do not have dependencies in the order of closing, though it is most common that inventory period is closed after purchasing.
There is a good advisor available in EBS that discuss and advise best practice for period close in the following note:
Period Close Advisor: E-Business Suite (EBS) (Doc ID 335.1)
Hope this helps.