Usually the peak seasons to go to Asia are:

Summer: June 1 - Sept 30
Christmas: December 15 - Jan 15
Chinese New Year - Late Jan to Feb depending on lunar N.Y.

These are usually the times that Asian airlines-China/EVA/SQ/Maylaysia raise their fares. If you can go any other time I would do it as many Y fares double (yup, they are twice as much. I.e. TPE/Hong Kong $500 low season and $1000 peak season) during peak vs. nonpeak.

Business class fares, however, usually remain constant at about $2k