I have intuition that cointegration between elements of pair of equities somehow contradicts pairs trading strategies. Because the better is linear fit of the model the less opportunities we have for arbitrage (with still holding assumption of stationarity of residuals).
For me it seems that it would be better (from trading point of view) to fit model which assumes that residuals follow autoregressive mean-reverting process (which looks like sinusoid or randomly alternating version of it)
primary school justification of my question in R :
set.seed(123) N=120 x1 <- cumsum(rnorm(N, sd=0.24)) SIN <- sin(seq(0, 20, length.out=N)) x2 <- x1+SIN+rnorm(N, sd=.2) matplot(cbind(x1, x2, SIN), t="l") abline(h=0, col=3)
if residuals are not correlated isn't it harder to select entry and closing points of pairs trading strategy ?