You could just use a particle emitor attach it to the camera so that it always moves with the camera and have the particle emitor box big enough so that it emits all above the view port and tell the particles to move down, if you have Unity Pro, you can use a separate camera so that you can add Motion bluer to get the streaky look, otherwise it might look more like snow.

Can you explain to me why it should be attached to a camera? I want this trail to stay in one place but give the illusion that the particles are floating.

I'm sorry, I have no experience at all with this :)