Long post, but kind of a simple question: I have two processes, x and y. I put them into a multivariate process, looking for a VAR(p), and find that there are no significant autocorrelations at all. Note though, that x and y are I(1), in that one differencing results in stationarity. x(t) = u1(t) + WN1(t) y(t) = u2(t) + WN2(t) Where WN = white noise. u1 and u2 are random walks, or "stochastic trends". If I look for a cointegrating vector, I am looking for some vector Transposed[ [alpha, beta]] such that: alpha * x(t) + beta * y(t) is I(0) -- or stationary. So I go back to the original case and subtract the two processes: beta*y(t) + alpha*x(t) = (u2(t) + WN2(t)) + (u1(t) + WN1(t)) Rearrange terms: beta*y(t) + alpha*x(t) = (u2(t) + u1(t)) + (WN2(t) + WN1(t)) For convenience, I say alpha = 1, so: beta*y(t) + x(t) = (u2(t) + u1(t)) + (WN2 + WN1) so: x(t) = (u2(t) + u1(t)) + (WN2(t) + WN1(t)) - beta * y(t) Now we have a sum of two random walks, both functions of time, the sum of two white noise processes, minus beta * y(t), where beta is the second component of some mystery cointegration vector. Clearly, we have non-stationarity here because there are two RWs with drifts, two white noise processes, and some beta. The drifted random walks account for the stochastic trend. But since we know the random walks step in time in such a manner that each step is sampled from the same distribution, ... then: x(t) = u2(t) + u1(t) + (WN2+WN1) - beta * y(t) and: x(t-1) = u2(t-1) + u1(t-1) + (WN2(t-1) + WN1(t-1)) - beta * y(t-1) Now if I difference x(t) and x(t-1): delta[x(t)] = rwstep1 + rwstep2 + net_errorterm - beta * ( delta[y] ) where: rwstep1 + rwstep2 are both stationary processes, the "differenced" stochastic steps, and delta is the differencing function, and the net error term is just the differences of the errors. If rwstep1, rwstep2, net error term are all I(0) stochastic processes and they are all independent, ... can I lump them together such that: delta[x(t)] = stochastic_lump - beta * delta[y], and still run around telling people that the beta I've got in this case is not some spurious relation, if, in fact, the t-test on the regression coefficient shows that it is significant? I just need some help here with cointegration theory when I have this degenerate case with no AR(p) coefficients.