Ticking noise coming from engine bay?

I own a 2000 Honda civic si and as of recently there's been a ticking noise. The noise comes on whenever I cold start my car and when I'm accelerating past 2,500 rpms. The noise is like a ticking/rattling noise. When i cold start it, the ticking is really fast. The thing is, when the car is cold and I'm driving it cold, it won't make the ticking noise, only at start up. When the car is warmed up, the ticking noise doesn't appear at start up, it only appears when I drive it. Any one have any ideas what it might be? Thank you in advance.
Points to remember:
- Cold start=Noise
-warm start=no noise
-driving cold=no noise
-driving warm= noise at 2500rpms+

Get your valves adjusted. A routine job on older Hondas.

Have it checked at your local mechanic/gas station.

It sounds like a lifter is collapsing under certain circumstances. But the first thing to do is remove the serpentine belt in the morning and see if the noise is there to eliminate, that will take out a pulley or tensioner. If the noise is still there then I'm almost sure it would be a lifter.