Why is DC component ignored and AC analysis is used when obtaining input output impedance of a BJT transistor amplifier?
The amplifiers you are speaking of are audio, that is, they only concern themselves with AC. As such, they are ordinarily AC coupled at both input and output with capacitors. So their DC input impedance is expected to be infinite, and their DC output impedance infinite.

EDIT - You added your schematic while I was composing this. Note the input and output capacitors. END EDIT 

For amplifiers which are expected to include DC, DC input impedance must be specified, and likewise output impedance. You'll see both of those addressed in the data sheets of operational amplifiers. For inputs, you'll see specifications for input offset voltage, input offset current, and input bias current. For outputs, you'll commonly see the maximum voltage swing available for one or more load resistors, which is directly related to output impedance (although the presence of loop gain complicates the matter).