Is timeline keyframe move on local space possible?

Is it possible to make keyframe anims behave on local space? I have a keyframe that animate the position of the object. It is parented to the timeline so i thought it would move along the parent. But it seems to be staying on a same place where i animated it.

The reason i want to do this is to make use of timeline's features. Where i can place the director's transform anywhere i want and play with the animation i made inside my timeline. I understand that the position key can override its local position, but i hope there's another way to avoid this.

I hope i can recieve reponse from here and thank you for taking time reading this!

 

This is very embarrassing, I'm sorry i posted it here, but i found that the object i thought was not moving with the director's transform is not nested that's why it doesn't move along.
You can delete this thread Admin if you want.
Thanks!