# Cointegration and pairs trading

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 ?

• I don't understand the distinction you are making. A stationary process with zero mean does look like "a sinusoid or randomly alternating version if it". An ARMA process is just one example (in discrete time) of a stationary process, the simplest example (because it is linear in form). – Alex C Mar 19 '17 at 15:47
• @Alex C I think you are quite right, but from technical point of view I'm not sure if the ARMA could reproduce sinusoid (I will try and expand question), and expecially if it can reproduce randomly alternating sinusoid – Qbik Mar 19 '17 at 16:13