regression with constraints

[comeon2012]

Hi all,

In the attached example, there are dayily trading data for two mutual funds in different months. But in my whole sample, there are daily data for various funds in many different months.

I want to run a regression model as below:

y= b1*x1 + b2*x2 + b3*x3 + b4*x4 + b5*x5 + b6*x6 + b7*x7 + b8*x8 + e

It is not a ordinary regression model but with contraints:

s.t. (1) b1, b2, ..., b8>=0

       (2) b1+b2+, ..., +b8=1

min Var（e）

When running this regression, I also want to generate a new data file consisting of coefficients, t and p value from each regression on each fund in each month.

for example,

regress when fundcdym=000001200507 (fund 000001 in July 2005), there are 21 obs and the regression result inclueds coefficients, t and p value.

regress when fundcdym=000001200508 (fund 000001 in July 2005), there are 23 obs and the regression result inclueds coefficients, t and p value.

...

Can anybody help me to deal with this? Thanks in advance.

[PGStats · Accepted solution]

I tried the following with SAS/ETS proc Model but didn't find the results very convincing (given your constraints and your number of observations in each month, I am not certain there can be meaningful OLS solutions)

data rwc;

infile "&SASFORUM\datasets\regression with constraints.csv" dsd firstobs=2;

length fundcd ym $6 Fundcdclsdt fundcdym $12;

input FUNDCD CLSDT :yymmdd10. Fundcdclsdt ym fundcdym y x1-x8;

run;

proc model data=rwc plots=none;

by fundcdym notsorted;

y= b1*x1 + b2*x2 + b3*x3 + b4*x4 + b5*x5 + b6*x6 + b7*x7 + b8*x8;

bounds 0 <= b1-b8;

restrict b1+b2+b3+b4+b5+b6+b7+b8 = 1;

fit y / outest=rwcfit;

ods output ParameterEstimates=rwcPE;

run;

PG