the answer to this riddle is carpet
A rug
The answer to your riddle is "stairs." Stairs allow people to go up and down between levels, yet they themselves remain stationary. The word "stairs" consists of six letters.
The answer to this riddle is "a staircase". Of course the staircase does not actually move up and down, but when you refer to a staircase directionally, you are either going "up the stairs" or "down the stairs". Its function in and of itself is to "go" up and down.
The railing
A stock market, it goes up and down but never move
Your Jaw.
Stairs, you go up you go down but the stairs never move.
An Elevator
stairs
steps
An escalator is a moving staircase that transport people vertically between floors without requiring them to walk, while a lift (elevator) is a compartment or platform that moves vertically within a shaft to transport people and goods between different floors of a building. Essentially, an escalator moves people continuously, while a lift moves intermittently between floors.
A news paper!