GLS and Prais-Winsten AR(2)

[ch2324]

Hi every body,
when i have first order autocorrelation in simple linear regression (y=a+b*x) i can transforme the variables by this way, or appending the term ar(1).

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e=c(1)*e(-1) scalar p=c(1) smpl 1 1 series yy=((1-p)^0.5)*y series xx=((1-p)^0.5)*x series const=((1-p)^0.5) smpl 2 @last series yy=y-p*y(-1) series xx=x-p*x(-1) series cont=1-p smpl @all yy const xx

suppose now i have the second order autocorrelation ar(2), i can make transformation or appending the term ar(1) ar(2).

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e=c(1)*e(-1)+c(2)*e(-2) scalar p1=c(1) scalar p2=c(2) smpl 1 1 series yy={(1+p2)*[(1-p2)^2-p1^2]/(1-p2)}^0.5*y series xx={(1+p2)*[(1-p2)^2-p1^2]/(1-p2)}^0.5*x series const={(1+p2)*[(1-p2)^2-p1^2]/(1-p2)}^0.5 smpl 2 2 series yy=(1-p2^2)^0.5*y2-[p1*(1-p1^2)^0.5/(1-p1)]*y1 series xx=(1-p2^2)^0.5*x2-[p1*(1-p1^2)^0.5/(1-p1)]*x1 series const=(1-p2^2)^0.5-[p1*(1-p1^2)^0.5/(1-p1)] smpl 3 @last series yy=y-p1*y(-1)+p2*y(-2) series xx=x-p1*x(-1)+p2*x(-2) series const=1-p1-p2 smpl @all yy const xx

my two questions:
(*) when i use smpl 2 2 i can not multiply y1 x1 (first obs of variable y and x), how can do this?
(**) when i appending ar(1) ar(2) whith CLS method i lose 2 obs, but i can use GLS method to keep the 2 obs, is this the Prais-Winsten procedure in EViews to transforme directly the two first obs?

Best Regards CHERIF.