A Gulfstream-V flight crew departed an intermediate altitude prior to complying with an ATC crossing restriction. Faulty or improper FMS programming may have contributed.

Narrative

We were flying to TEB on the JAIKE TWO ARRIVAL and had been stepped down to cross JAIKE at 13;000 which we did. We were then cleared to descend on the JAIKE TWO ARRIVAL. With the concurrence of my Co-pilot; we selected 7000 on the altitude alerter and armed VNAV for the programmed descent. I had checked and verified with the copilot that all of the crossing restrictions were correctly loaded in the FMS. When the autopilot started a descent I began to crosscheck that we were on profile and had just noticed that we were starting down before the crossing restriction of 13;000 over ILENE. I realized that we were early and disconnected the autopilot. As I was starting a climb from around 12;500 to return to 13;000 ATC called and said that we had started down early and issued a clearance to cross ILENE at 12;000. We complied with this revised clearance and flew the rest of the profile descent without VNAV guidance. No conflicts were observed and ATC made no mention of any loss of separation. I believe several factors contributed to this event: 1. Prior to this happening the FMS had been acting up on takeoff and climb out by not commanding the proper autospeeds and the autopilot had disconnected without any warning. This should have been enough of a heads up to more closely monitor the FMS for any performance errors. On the next leg the FMS worked perfectly as it had on the previous legs. 2. I had not flown in a month. This; coupled with the fact that I got to the airport and joined the crew ready for an immediate taxi out and takeoff; meant that a lot was coming at me fast in this short leg. 3. We use an EFB and I wasn't referencing a paper chart. With a paper chart I would have had the crossing restrictions highlighted so I may have noticed earlier that ILENE had to be crossed at 13;000. 4. At the time we armed VNAV for the vertical descent it occurred to me to change the cruise altitude in the CRUISE page to 13;000 but I didn't. I confirmed with my Copilot that everything looked good for VNAV to fly the profile as it was programmed and it was our expectation that it was going to do the step downs without making any other entries. In retrospect; I wish I had changed the CRUISE page to 13;000 because that may have reset the computer's calculations; which obviously turned out to be wrong.