Hi Atif,
You can indeed work with budget period, which was developed for monthly or other periodical budget management. However, even with this object, there is no functionality of automatic carry-over of the budget. Budget carry-over is relevant only for year dimension; all other operations would be handled via budget transfer. You can, though, develop a job, which would transfer residual budget from budget period X to X+1, and you can schedule this job in the end of each month.
Regards,
Eli