Suppose we have sales of 3 products A, B and C which market share always sum up to 100%. How to model market share of product A using market shares of B and C? So that we will know that if share of A grows 1 percentage point then A has to steal that growth in some proportion form products B and C.
A means increase of share = A on Tuesday - A on Monday, and so on with B, C.
A = 0*A + b1*B + c1*C B = a2*A + 0*B + c2*C C = a3*A + b3*B + 0*C b1+c1=-1 a2+c2=-1 a3+b3=-1
How to estimate it? Is there any other method how to estimate structure which sums to 100% by the parts of the structure? Regression doesn't work here.