Can I deduce ‘Z’ with just A, B and C? I don't have access to x and y series.
No, because A,B,C and y1,y2,y3 determine the x's. So fix A,B,C and take two different sets of values for y1,y2,y3 that give different valuse for Z. Then corresponding x's can be found so that you have different Z's corresponding to the same A,B,C