Hi Kwen,
The behavior for costing is depending on the costing model you are using. You can read the Cost management whitepaper to get an understanding. This document was written for AX2009, but is still applicable. A new moving average model was introduced in AX2012.
When you use a costing method which needs recalculation and closing, the recalculation can run every night, but can also be setup to run weekly, depending on your needs. The closing should run at least every period for your month end procedure. Depending on the number of transactions that needs to be closed, it can be setup to run weekly.