One trick to use for this type of problem is to transform the regression.
So if we want to regress y against x1, x2 and x3 and constrain the
parameters to sum to 1 we do the following,
Subtract x1 from each of the other variables so we have y-x1, x2-x1, x3-x1
Regress y-x1 against the other two variables (no constraints needed unless
you want all the parameters to be positive).
y-x1 = A + B(x2-x1) + C(x3-x1) +e
Rearranging the results gives us
y = A + x1(1-B-C) + Bx2 + Cx3 +e
Thus the parameters sum to 1.
The only problem in your case is that it would be easier to program if you
have one variable (x1 in the above case) that is always present on the RHS
of the regression.
Charles Ward
On 29 August 2012 14:38, Jan Tille <Jan.Tille(a)absolut-research.de> wrote:
 Dear gretl users,
 first of all let me thank you, that you have already provided me with
 solutions on other topics. Unfortunately, I need your help again.
 The problem I am now trying to solve is the following.
 Basically, I want to set up a rolling regression with parameter
 restrictions (all parameters, except for the constant shall sum to one) and
 store the coefficient estimates. So far this poses no problem:
 <hansl>
 Matrix C={}
 List indep=indep1..indep10
 Smpl 1 36
 Loop i=1..360
         Ols dep const indep
         Restrict
                 b[2]+b[3]+b[4]+b[5]+ b[6]+b[7]+b[8]+b[9]+b[10]=1
         end restrict
         Matrix c=coeff'
         C=C|c
         Smpl +1 +1
 Endloop
 </hansl>
 But as you can see, I have lots of regressors and not all might be
 significant, or depending on the time window the significance will change.
 I know that I can use the omit --auto function to select only significant
 coefficient estimates, but here it is, where the problems start:
 1.) Assume that during the first window, there are 3 significant
 coefficients, so that the matrix will have 3 columns. If it should be, that
 during the next time window, there are, say 4 significant coefficients,
 then the script breaks down (matrices do not fit). Therefore, I guess I
 have to reshape the matrix somehow, to allow for the new column.
 2.)Assume that during the first window there are 3 significant
 coefficients (2, 3, 4) and during the next time window there are 3
 different significant coefficients (6,7,8). Then, the dimension of the
 matrix would be correct, but interpreting the matrix of coefficients
 afterwards in a time series context would not make much sense.
 To summarize 1.) and 2.), I would need a matrix with 10 columns, where
 "NA" is entered, if the respective coefficient is insignificant and else
 the coefficient. So that one can obtain the time series of significant
 regressors.
 Date    indep1  indep2 ...      indep10
 1       0,8             0,1             0,1
 2       0,6             NA              NA
 3       0,75            NA              0,05
 The third issue arises with the parameter restriction. After omitting
 insignificant variables, the restriction that coefficients sum to one
 should still apply.
 Unfortunately there seems to be no simple shortcut for the restriction
 (for example restrict sum(coeff(2..n))) , whith n being the last
 significant coefficient).
 As I don't know ex-ante which parameters would be significant, I somehow
 have to dynamically readjust the restriction. Is there a way how one can do
 it?
 Thanks in advance for your time answering my questions.
 Kind regards,
 Jan
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