'''program compare_Lc uses single equation shortcuts ''''Begins by creating workfile and generating simulated data y x1 x2 '''The Lc stat as calculated here is scalar named a_Lc, must compare to Eveiws calculation by opening equation named e_eviews '''Have confirmed that the approach taken below to calculate a_Lc yields same results if I calculate Lc using (@transpose(bigS_t))*(@inverse(G))*bigS_t '''Results for b-hats are equal to those of eviews, compared by vector named diff '''For Lc results differ from eviews by +-0.01 or better, scaling by 1/!N rather than 1/!T, AND using all observations in calculating M or G '''follows eviews in placiing constant last '''April 11, 2012 '''SEE PROGRAM LC_EV_H_CONSISTENT2F, E, D, ... FOR COMPARISON TO EVIEWS approach to LC ETC !N = 100 ''''this determines sample size 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 '''''should be and is near 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 matrix M = Z*(@transpose(Z)) matrix first = @inverse(M) !T = @columns(Z) '''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 Zy = Z*yy_plus vector second = Zy -lam '''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 '''''y-hat from fmols vector u_plus = yy_plus - yhat_plus '''''residuals from fmols '''''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) matrix(!T,3) bigU ''''will have identical !Tx1 columns of u+, makes it easier to construct X-var columns multiplied by residuals colplace(bigU,u_plus,1) colplace(bigU,u_plus,2) colplace(bigU,u_plus,3) matrix Zu = @emult((@transpose(Z)),bigU) ''''this is almost the score vector, but each row needs adjustment by lam12_plus: '''next need to subtract lam_noT from each element vector(!T) lamplus1 = lam12_plus(1) vector(!T) lamplus2 = lam12_plus(2) matrix(!T,3) lamplus '''''this matrix will be !Tx1, columns of lam12_plus(1), lam12_plus(2), 0 (next two lines) colplace(lamplus,lamplus1,1) colplace(lamplus,lamplus2,2) matrix small_s_transpose = Zu -lamplus ''''this is !T by 3 matrix small_s = @transpose(small_s_transpose) '''this is 3 by !T, used below in big_S '''''''''''''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 ''''''''''''''calculate M = X'X, using all observations of X smpl 1 !N genr ones = 1 group gx x1 x2 ones matrix bigZ = @convert(gx) ''''data in rows by observation as usual, bigZ is the usual ols X matrix matrix bigM = (@transpose(bigZ))*bigZ '''''Lc using Hansen's approach, I have confirmed that get same value using (@transpose(bigS_t))*(@inverse(G))*bigS_t as in Eviews documentation matrix H = (1/omega1_2)*Big_S*(@transpose(Big_S)) matrix Lc_H_M = (@inverse(bigM))*H scalar a_Lc = (@trace(Lc_H_M))*(1/!N) ''''''THIS COMES CLOSE TO REPRODUCING EVIEWS VALUES uses M employing all obs of x, scale by !N, not !T '''this equals alt_Lc_e_fix in previous program