Multivariate Regression with coeffcients constrained to lie on a k polynom

I would like to run a regression of age cohorts in % (x1,x2,x3) on the a return level (20yr time series), including a control variable in the regression for the interest rate level. The coefficients of these age cohorts are constrained to satisfy a polynomial of order k. The coefficients are in addition constrained to sum to 0. Any help much appreciated.

Answer 1

[Roger Wohlwend]

You have to use optimization for your Problem. Use the Matlab function fmincon.

[Oli]

Roger, thank you very much. It would be very helpful if you could be a little bit more specific. I guess I have to use the function polyfit in connection with fmincon. But how can I combine the multivariate regression (5 age cohorts: 1-10y, 10-40y,40-60y,60-70y, 70y+) on variable y over 20 time periods with the constraint that the 5 variables should lie on a 3th order polynomial and constrained in sum to 1? I am struggling how to construct the logic of this function. Any advice would be very much appreciated.