Rendering Background Layer with Camera Shaking Effect

I have just began to work with rendering separate layers of a scene in Blender. I am making a little animation, which has a still background, but the camera is animated to shake a few centimeters up and down, left and right for part of the animation.

Is there a way to render the background layer just once and obtain the shaking effect by some other means (perhaps, render a bigger frame and then cut smaller frames or something like that)? Or the only way is still to render each small camera move as a separate background layer frame? Thanks in advance!

Make everything invisible for render and render your shaking background… but in the end you have to compose your background with your foreground…