How to get date an interval of Date using the Time class?

Hi, I would like to use the Time class provided by CodeIgniter to easily translate the name through the "toLocalizedString" method.
Unfortunately, I didn't found any method that allow me to create a period of dates, could someone tell me how can I replicate this code using the Time class?

PHP Code:

$period = new DatePeriod(
     new DateTime('2010-10-01'),
     new DateInterval('P1D'),
     new DateTime('2010-10-05')
); 


Thanks