'''program Lc_ev_H_consistent '''avoids shortcuts of previous programs ''''Get consistent results with eviews and Hansen approach for Lc, but value is scaled too large by (!N+2) to (!N+2.5) '''follows eviews in placiing constant last ''''based on program FMOLS_e01 !N = 100 WFcreate u !N smpl 1 1 genr x1 = 10 genr x2 = 2 smpl 2 !N genr x1 = x1(-1) +nrnd genr x2 = x2(-1) +nrnd genr cx1 = x1 -x1(-1) genr cx2 = x2 -x2(-1) smpl 1 1 genr rr = (9/8)*nrnd smpl 2 !N genr rr = 0.8*rr(-1) +0.5*nrnd smpl 1 !N genr y = 5 +0.3*x1 -0.3*x2 +rr '''autocorrelated errors in cointegration process (else fmols has less to do) smpl 1 !N ls y c x1 x2 genr u1 = resid smpl 2 !N genr u_x1 =cx1 genr u_x2 = cx2 group gu u1 u_x1 u_x2 '''group the cointegrating model and x-var residuals gu.lrcov(window=sym,lag=1,kern=bart,bw=fixednw,noc,out=omega) '''estimate long-run covariance, results placed in omega gu.lrcov(window=lower,lag=1,kern=bart,bw=fixednw,noc,out=lambda) '''estimate one-sided (lag) covariance, results placed in lambda. smpl 1 !N equation e_eviews.cointreg(method=fmols, trend=const, regdiff, lag=1, kern=bart, bw=fixednw) y x1 x2 vector(3) b_eviews b_eviews(1) = e_eviews.@coefs(1) ''''eviews lists constant last b_eviews(2) = e_eviews.@coefs(2) b_eviews(3) = e_eviews.@coefs(3) matrix e_omega = e_eviews.@lrcov '''''eviews cointreg proc est of lrcov matrix e_lambda = e_eviews.@lambda12cov ''''eviews cointreg proc est of one-sided matrix p_lambda = @subextract(lambda,1,2,3,3) '''omits first column of one-sided lrcov as generated by LRCOV command matrix dif_omega = e_omega -omega '''''Difference between calc by LRCOV and calc by COINTREG, should be zero matrix dif_lambda = e_lambda -p_lambda '''''also should be zero scalar omega11 = @subextract(omega,1,1,1,1) ''''scalar rowvector omega12 = @subextract(omega,1,2,1,3) ''' 1x2 vector omega21 = @subextract(omega,2,1,3,1) ''' 2x1 matrix omega22 = @subextract(omega,2,2,3,3) ''''2x2 rowvector Q = omega12*(@inverse(omega22)) '''part of calculating yplus and lambda12_plus and omega1_2 In Hansen's programs this is "g" genr y_plus = y - (Q(1)*u_x1 +Q(2)*u_x2) rowvector lambda12 = @subextract(lambda,1,2,1,3) '''eviews w12 matrix lambda22 = @subextract(lambda,2,2,3,3) rowvector lam12_plus = lambda12 -(Q*lambda22) ''''used below in bhat calc, this is lamda12 plus in eviews exposition scalar temp = Q*omega21 scalar omega1_2 = omega11 -temp '''' smpl 2 !N genr ones = 1 group gx x1 x2 ones matrix Z = @transpose(@convert(gx) ) ''''a column for each observation t vector yy_plus = @convert(y_plus) '''series put into vector ''''''''''''''''''''''' b-hat needs two summations observation by observation !T = @columns(Z) matrix(3,3) sumZZ '''this will store sum Zt*Zt' vector(3) sumZy '''this will store sum z*yyplus For !col = 1 to !T vector Zt = @columnextract(Z,!col) matrix ZZ = Zt*(@transpose(Zt)) '''this should be 3 by 3 sumZZ = sumZZ +ZZ '''acumulate sum vector zy = Zt*(yy_plus(!col)) '''3 by 1, is Z*y_plus at date t sumZy = sumZy + zy ''''accumulte sum Next '''''note in single equation case then could calc sumZZ = Z'*Z '''need to take inverse of sumZZ matrix first = @inverse(sumZZ) '''this is first expression in b-hat matrix M = sumZZ '''used below in Hansen's and Eviews Lc calc '''need to modify sumZy by transpose of T*(lambda12_plus, 0 ) vector(3) lam '''note last element is zero lam(1) = !T*(lam12_plus(1)) lam(2) = !T*(lam12_plus(2)) vector second = sumZy -lam ''''this is second expression in b-hat vector b_hat = first*second vector diff = b_hat -b_eviews '''this comparison of my vs Eviews b-hats should be near zero, and it is '''''''''''''''''''''''''''End b-hat calc, now try Lc'''''''''''''''''''''''''''''''''' vector yhat_plus = (@transpose(Z))*b_hat vector u_plus = yy_plus - yhat_plus '''''each small s(t) is 3 by 1, but here make a 3 by T matrix of all the s(t)'ies matrix(3,!T) small_s vector(3) lam_noT lam_noT(1) = lam12_plus(1) lam_noT(2) = lam12_plus(2) For !col =1 to !T vector Zt = @columnextract(Z,!col) ''''column vec at t vector temp_s = Zt*u_plus(!col) -lam_noT '''this is an s(t) small_s(1,!col) = temp_s(1) small_s(2,!col) = temp_s(2) small_s(3,!col) = temp_s(3) Next '''''end of making matrix of small s(t) '''''''''''''next need to make matrix of the Big S, which are partial sums of s Matrix(3,!T) Big_S vector(3) temp_sum For !col = 1 to !T vector s_t = @columnextract(small_s,!col) temp_sum = temp_sum +s_t Big_S(1,!col) = temp_sum(1) Big_S(2,!col) = temp_sum(2) Big_S(3,!col) = temp_sum(3) Next '''a check is that last column should equal zero ''''''''Now need M which is sum Zt'Zt in contrast to sumZZ which is sum ZtZt' '''and need G which is omega1_2 times sum ZtZt' = M matrix G = omega1_2*M ''''''Eviews Lc scalar Lc_e '''will store the sum of which the trace is Lc For !col = 1 to !T vector bigS_t = @columnextract(Big_S,!col) matrix temp_Lc = (@transpose(bigS_t))*(@inverse(G))*bigS_t Lc_e = Lc_e +temp_Lc(1,1) Next '''NOTE final Lc_e is approach to calculating Lc as described in eviews documentation ''''end Eviews Lc '''Hansen Lc scalar Lc_H '''Hansen's exposition matrix(3,3) temp_HH For !col = 1 to !T vector bigS_t = @columnextract(Big_S,!col) matrix tempH = bigS_t*(1/omega1_2)*(@transpose(bigS_t)) temp_HH = temp_HH +tempH Next matrix H = (@inverse(M))*temp_HH Lc_H = @trace(H) '''end Hansen Lc ''' My Lc_e = Lc_H, but these are much too large. Scaling by (1/(!T+k)) almost, but does not fix the problem. Somewhere I am missing a scale factor and I think some constant term also.