$TITLE  StoNED example


SETS
i                observations /i1*i88/
;

alias(i,j)
;

PARAMETERS
Y(i)           output
X1(i)           input
X2(i)           input
X3(i)           input
X4(i)           input
X5(i)           input


SSvalue                     additional export var for SS
Evalue(i)                    additional export var for E
Avalue(i)                    additional export var for A
B1value(i)                    additional export var for BL
B2value(i)                    additional export var for BL
B3value(i)                    additional export var for BL
B4value(i)                    additional export var for BL
B5value(i)                    additional export var for BL
;



$libinclude xlimport Y C:\GAMS\GAMSFILES\SUV\NPV.xls a1:cj2
$libinclude xlimport X1 C:\GAMS\GAMSFILES\SUV\CO2.xls a1:cj2
$libinclude xlimport X2 C:\GAMS\GAMSFILES\SUV\NOX.xls a1:cj2
$libinclude xlimport X3 C:\GAMS\GAMSFILES\SUV\HC.xls a1:cj2
$libinclude xlimport X4 C:\GAMS\GAMSFILES\SUV\Part.xls a1:cj2
$libinclude xlimport X5 C:\GAMS\GAMSFILES\SUV\Noise.xls a1:cj2
;




VARIABLES
E(i)             error term
A(i)             constant
SS              sum of square of errors
;


POSITIVE VARIABLES
B1(i)           beta coefficients (positivity quarantees monotonicity)
B2(i)           beta coefficients (positivity quarantees monotonicity)
B3(i)           beta coefficients (positivity quarantees monotonicity)
B4(i)           beta coefficients (positivity quarantees monotonicity)
B5(i)           beta coefficients (positivity quarantees monotonicity)

;


**** formula's for calculating CSLS***
EQUATIONS
QSSE             objective=sum of squares of errors
QREGRESSION(i)        regression equation
QCONCAVITY(i,j)   concavity constraint;

QSSE..           SS=e=sum(i,E(i)*E(i));
QREGRESSION(i)..      Y(i)=e=A(i)+B1(i)*X1(i)+B2(i)*X2(i)+B3(i)*X3(i)+B4(i)*X4(i)+B5(i)*X5(i)+E(i);
QCONCAVITY(i,j)..   A(i)+B1(i)*X1(i)+B2(i)*X2(i)+B3(i)*X3(i)+B4(i)*X4(i)+B5(i)*X5(i)=l=A(j)+B1(j)*X1(i)+B2(j)*X2(i)+B3(j)*X3(i)+B4(j)*X4(i)+B5(j)*X5(i);

MODEL CNLS /all/

OPTION limrow    = 0;
OPTION limcol    = 0;
OPTION SOLPRINT  = OFF;
OPTION optcr     = 0.0;
OPTION iterlim   = 10000000;
OPTION reslim    = 10000000;

$libinclude gams2txt


SOLVE CNLS using NLP Minimizing SS;
SSvalue=SS.l;
Avalue(i)=A.l(i);
Evalue(i)=E.l(i);
B1value(i)=B1.l(i);
B2value(i)=B2.l(i);
B3value(i)=B3.l(i);
B4value(i)=B4.l(i);
B5value(i)=B5.l(i);

$libinclude xldump SSvalue C:\GAMS\GAMSFILES\SUV\CNLSresults.xls ss a1:cw120
$libinclude xldump Avalue C:\GAMS\GAMSFILES\SUV\CNLSresults.xls A a1:cw120
$libinclude xldump Evalue C:\GAMS\GAMSFILES\SUV\CNLSresults.xls E a1:cw120
$libinclude xldump B1value C:\GAMS\GAMSFILES\SUV\CNLSresults.xls B1 a1:cw120
$libinclude xldump B2value C:\GAMS\GAMSFILES\SUV\CNLSresults.xls B2 a1:cw120
$libinclude xldump B3value C:\GAMS\GAMSFILES\SUV\CNLSresults.xls B3 a1:cw120
$libinclude xldump B4value C:\GAMS\GAMSFILES\SUV\CNLSresults.xls B4 a1:cw120
$libinclude xldump B5value C:\GAMS\GAMSFILES\SUV\CNLSresults.xls B5 a1:cw120



OPTION decimals=7;