GMM and covariance among factors
Posted: Thu Jun 06, 2019 2:48 pm
Given the 7 variables (y1,...,y7) and the tree factors (x1, x2 and x3), is it possible to save the covariance of factors x1, x2 and x3 using GMM, after solving the system below?
system SDF
SDF.append ( y1*(1 - c(1)*(x1 - c(4)) - c(2)*(x2 - c(5)) - c(3)*(x3 - c(6))) ) = 0 @ c
SDF.append ( y2*(1 - c(1)*(x1 - c(4)) - c(2)*(x2 - c(5)) - c(3)*(x3 - c(6))) ) = 0 @ c
SDF.append ( y3*(1 - c(1)*(x1 - c(4)) - c(2)*(x2 - c(5)) - c(3)*(x3 - c(6))) ) = 0 @ c
SDF.append ( y4*(1 - c(1)*(x1 - c(4)) - c(2)*(x2 - c(5)) - c(3)*(x3 - c(6))) ) = 0 @ c
SDF.append ( y5*(1 - c(1)*(x1 - c(4)) - c(2)*(x2 - c(5)) - c(3)*(x3 - c(6))) ) = 0 @ c
SDF.append ( y6*(1 - c(1)*(x1 - c(4)) - c(2)*(x2 - c(5)) - c(3)*(x3 - c(6))) ) = 0 @ c
SDF.append ( y7*(1 - c(1)*(x1 - c(4)) - c(2)*(x2 - c(5)) - c(3)*(x3 - c(6))) ) = 0 @ c
SDF_all_{%type}.append ( X1 - c(4) ) = 0 @ c
SDF_all_{%type}.append ( x2 - c(5) ) = 0 @ c
SDF_all_{%type}.append ( x3 - c(6) ) = 0 @ c
param c(1) 0.9 c(2) 0.9 c(3) 0.9 c(4) 0.9 c(5) 0.9 c(6) 0.9
'Sequential weighting matrix & coefficient iteration
'Cross section (White Cov) will result in GMM estimates robust to heteroskedasticity of unknown form
SDF_all_{%type}.gmm(instwgt=white,method=nstep,wtype=istdev,s)
system SDF
SDF.append ( y1*(1 - c(1)*(x1 - c(4)) - c(2)*(x2 - c(5)) - c(3)*(x3 - c(6))) ) = 0 @ c
SDF.append ( y2*(1 - c(1)*(x1 - c(4)) - c(2)*(x2 - c(5)) - c(3)*(x3 - c(6))) ) = 0 @ c
SDF.append ( y3*(1 - c(1)*(x1 - c(4)) - c(2)*(x2 - c(5)) - c(3)*(x3 - c(6))) ) = 0 @ c
SDF.append ( y4*(1 - c(1)*(x1 - c(4)) - c(2)*(x2 - c(5)) - c(3)*(x3 - c(6))) ) = 0 @ c
SDF.append ( y5*(1 - c(1)*(x1 - c(4)) - c(2)*(x2 - c(5)) - c(3)*(x3 - c(6))) ) = 0 @ c
SDF.append ( y6*(1 - c(1)*(x1 - c(4)) - c(2)*(x2 - c(5)) - c(3)*(x3 - c(6))) ) = 0 @ c
SDF.append ( y7*(1 - c(1)*(x1 - c(4)) - c(2)*(x2 - c(5)) - c(3)*(x3 - c(6))) ) = 0 @ c
SDF_all_{%type}.append ( X1 - c(4) ) = 0 @ c
SDF_all_{%type}.append ( x2 - c(5) ) = 0 @ c
SDF_all_{%type}.append ( x3 - c(6) ) = 0 @ c
param c(1) 0.9 c(2) 0.9 c(3) 0.9 c(4) 0.9 c(5) 0.9 c(6) 0.9
'Sequential weighting matrix & coefficient iteration
'Cross section (White Cov) will result in GMM estimates robust to heteroskedasticity of unknown form
SDF_all_{%type}.gmm(instwgt=white,method=nstep,wtype=istdev,s)