How are you this evening welcome to just awnser.
Was the issue happening before you tuned it up? watch what parts you use, poor quality parts from some of the auto stores can cause missfire issues. now you need to try a balance test when this happens find out if it is one or all the cylinders pull one wire off at a time while running (use pliers as to not get shocked) if no change in the engine rpm is found then you found the cylinder if you are getting spark plug the boot back on and pull the fuel injector plug if no change then you likley have a gumed up injector I like to listen to the injectors with along screw driver to my ear or a stethascope you should here a clicking they should all sound about the same.
There is some other things I would like to ask, Has the timing belt been done before if it slipped a tooth that will cause low power. also there is a service bulletin on bad exhaust valves. I leak down test will need to be performed to confirm this.
The last thing I would like to add is that, I have ssen alot of fuel injector issues when cold our ethanol in the fuel plugs up the injectors if it goes away as it warms up I would start here. If you put bosch parts on the car you may want to re-evaluate the tune up. Lots of issues with asian cars. Recommend NGK or Denso spark plugs they run the best. Champion is ok also.
i did not tune it up until the problems started. i have not done anything with the timing belt. The thing that gets me is it is intermittent and you never can tell when or where it might act up. Sometimes it has almost no power at all.
I would really consider doing a cylinder leak down test and looking into when the timing belt was done last if ever, backfiring is usually timing related or a problem with possible burnt valves. A leak done test will tell you if the cylinders are leaking, A quicker test would be a compression test but that only tells you what compression is in general and nothing about the cylinders condition. Does it do it in the morning when warming up, or when you just start it? Check the injectors and balance test when it is happening this will get you results also.
I have not tried any of this yet but it does seem to be much worse when it is cold
Catch it when it is cold it is probably missfiring at that time. Like I said take a long screw driver (if you do not have a stethascope) put it on the fuel injector body put your ear against it you should hear a clicking sound this is the injector opening. or the on off ( we call it duty cycle) if you do not hear clicking from one of the injectors that is your failure. If you listen to them all and hear a difference or one sounds like it is not keeping up with the others this could also be your issue also try to stick some BG 44k in the fuel tank this does help the injectors. Cheveron Techron is also very good its cheaper, but you need to use it more often.