Vinyl siding can be installed over sheathing, foam board or the old siding using 1x4 nail strips. What must be immediately under the siding is a moisture barrier, like Home Wrap. Fan-fold foam or foam panels can work as moisture barrier if properly taped when installed. I have a hard time believing the tape stays, but that is how they do it.
Today is PERFECT!
All information and advice given is for entertainment and informational purposes only. The person doing the work is solely responsible to insure that their work complies with their local building code and OSHA safety regulations.