Is it possible to upgade my iphone 4 on ios 4.2.1 to non ios7 version using jailbreak?

Hi. Wanna upgrade my iphone 4's ios version from 4.2.1 to 6.1.3. Is this possible using a jailbreak, despite the fact that the version isn't signed anymore? Or is this not possible anymore at all? New to jailbreaking, so don't know that much, and haven't been able to get anything concrete out of googling.

If possible, how do i go about this? If not possible, is my only choice of upgrading to a/any new version to go for the currently signed ones (7.1+)?