I have a few variables, $A$, $B$, $C$, $D$, and $E$. To find their cointegration coefficients, $A$ is regressed against $B$, $C$, $D$, and $E$. $$ A = W_b * B + W_c * C + W_d * D + W_e * E + W0 $$ (where $W_b$, $W_c$, $W_d$, $W_e$ are cointegration coefficients and $W_0$ is intercept). The residuals are then tested for stationarity.
The problem is that the cointegration coefficients are sensitive to the ordering of the variables. For example, if $B$ is regressed against $A$, $C$, $D$, $E$ I get a totally different set of coefficients.
How do I solve this problem?
Can I create a new variable, $X$ which has a constant value (either 0 or nonzero) and regress it against $A$, $B$, $C$, $D$, $E$? $$ X = W_a * A + W_b * B + W_c * C + W_d * D + W_e * E + W0 $$ Or should $X$ be a trending vector? (1,2,3,4,5,6,7,8......)
Can introduction of an artificial variable solve my problem or will it create more problems such as spurious regression?