HI All
I am having trouble in estimating R-Square according to Hasbrouck's RFS 1991 paper. I am trying to estimate the following equations:
VAR: [Equation:4]
r(t)= a1 r(t-1)+a2 r(t-2)+ ..... + b0 x(t)+ b1 x(t-1) +......+ v(1,t) ===> Eq 4 (a)
x(t)= c1 r(t-1)+c2 r(t-2)+ ..... + d1 x(t-1)+d2 x(t-2)+ ..... + v(2,t)
VMA: [Equation:5]
r(t) = v(1,t) + a*1 v(1,t-1) + a*2 v(1,t-2)+ .... ...+ b*0 v(2,t)+ b*1 V(2,t-1)+.....
x(t)= c*1 v (1,t-1)+ c*2 v (1,t-2)+ ... ..... + v(2,t)+ d*1 v (2,t-1) + d*2 v (2,t-2)+... ..
from equation 4 & 5 : I will estimate:
R-square (w)= Sigma-Square (w,x)/ sigma-square (w) --- eq(6)
where:
Sigma-Square (w,x)= (sum of b*(i)) * Omega * (sum of b*(i))(transepose);
Sigma-Square (w)= Sigma-Square (w,x) + (1+ Sum of a*(i))^2 * sigma-square (1); --- equation (7)
to estimate these I came up with the following SAS code:
/*First I simulate y1 and y2 to estimate a VAR*/
proc iml;
sig = {1.0 0.5, 0.5 1.25};
phi = {1.2 -0.5, 0.6 0.3};
call varmasim(y,phi) sigma = sig n = 100 seed = 46859;
cn = {'y1' 'y2'};
create a from y[colname=cn];
append from y;
quit;
/*I estimate VAR(4) model. */
/*The variance of error term for y1 and y2 are used in estimating R square*/
/*Problem:*/
/* 1) The above sas code does not estimate Eq 4(a) since my sas code does not include the contemporenous y2 terms */
/*2) I dont know how to modify the VARMAX to include the contemporaneous y2 term.*/
/*Please help me to solve this part*/
proc varmax data=a;
model y1 y2 / p=4 noint ;
ods output covInnovation=covInnovation;
run;
/*I then estimate the VMA process and saves the parameter estimates in PPP file*/
/*Problem*/
/* 1)There are convergence issue for one element of gradient. I dont know whether it can cause any problem*/ /*I dont know how to solve the convergence issue*/
/* 2)Is there any other way to estimate the coefficients b*(i) and a*(i) without doing the VMA */
proc varmax data=a;
model y1 y2 / q=4 noint ;
ods output ParameterEstimates=ppp;
run;
/*Please help me on this*/
/*This section I have used the parameters from the Original paper to estimate R-Square*/
/*I can replicate the result reported in the original paper. That means this code works.*/
/*Problem*/
/*How can I use the above two files to come up wit the following four parameter values : sumofcoeff_1, sumofcoeff_2, y1,y2*/
/*I want to write a sas code that will take these values from the saved files and use it to estimate R-Square*/
data test;
sumofcoeff_1=-0.272 ;
sumofcoeff_2=0.00164;
one_sumofcoeff_1= (1+sumofcoeff_1);
Sq_one_sumofcoeff_1= (one_sumofcoeff_1)*(one_sumofcoeff_1) ;
Sq_sumofcoeff_2= (sumofcoeff_2) * (sumofcoeff_2);
y1=0.00000556;
y2=.438;
sigma_wx= (Sq_sumofcoeff_2)* y2;
sigma_w= sigma_wx+ (Sq_one_sumofcoeff_1) * y1;
rsquare= sigma_wx/sigma_w;
run;
/*Please Help me */
::::::::::::::::::::::::::::::::::::::::::::::::
I have looked at Prof Hasbrouck’s Web site.. He has whole bunch of sas codes but I couldn't figure out which one I could use to get the RFS 1991 result.
If anyone has any clue please help me. I am struggling with this for long time.
I am not sure how Prof Hasbrouck’s Codes work.. How he manages to get b* and a* without doing any VMA. Is there any easy way round to find these coefficients.
Any help is highly appreciated
Thanks for the time
Abu S AMin
University of Houston
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