If the property was "placed in service" in December, you get a 1/2 month of depreciation (the first and last month only gets a 1/2 month of depreciation).
However, the depreciation starts when the property is "placed in service" (ready and available to be rented), not necessarily when you purchased it. So if it was not advertised for rent or available for people to move into it until 2018, it would not start until 2018.