Well, I answered in the comments but I'll answer here since I'm not liking any of the answers.

You do need to move the camera for a panning time lapse and you used to need a rig, motorized or not, rails or not, to do this movement. There is a new technique called hyperlapse or walklapse which accomplishes this without any extra equipment, aside from a tripod which you presumably already own.

You basically take the shot, move a few feet down the path you want the time-lapse to travel along, and then take the next shot. You make an attempt to frame the shots the same but you only need to get close.

When the shoot is done you load them into Adobe After Effects to clean it all up. Note, I've never ever done this, nor am I likely to, I've learned all about this technique from watching this video Here's a screen shot from the video:

The left hand side is the smooth, post processed video, the right hand side is a single from from the raw shoot. Notice how the wall and the boat do not line up, yet if you watch the final video the motion is smooth.