I look at Z-Score : Z(x) = (x-average(x))/stddev(x)
Price 1 -> Z1, Price 2 -> Z2
Positively correlated pairs Dislocation Metric = Z(Z1-Z2)
Negative correlated pairs Dislocation Metric = Z(Z1+Z2)
I know that neither price, nor log price, is really normally distributed, but this corrects the first two moments. it also allows me to plot several things on the same scale. If I size my legs inverse proportionately to volatility (stddev), then the profit/loss of the pair trade is accurately represented by the visual difference in the Z(prices).
The Dislocation Metric is then proportional to the profit/loss of the pair trade. It is more useful to scale it this way. Pair Trades between stock indices, for example, have Z(Price1)-Z(Price2) with a very small magnitude. For both highly positively correlated and highly negatively correlated markets, dividing out the standard deviation is essential to even vaguely judge statistically significance.
Low Z-scores should have low statistical significance. In practice, small(abs) Dislocation Metric values tend to have little predictability. Much like two houses jockeying for position at the nose.
High Z-scores should have high statistical significance. In practice, large(abs) Dislocation Metric values tend to revert. If a value gets too large, say +/- 4, I start to worry that the change has broken the underlying economic model. For example, a pair trade between Microsoft and DEC might have looked good fantastically profit potent until 1998 when Compaq bought it. Initially one could see the trade as two moving average (fast innovative poorly funded vs slow but well funded.) At some point, however, you have to say DEC is just not a competitor for Microsoft.
I allow, at various times, for detrending, logging, labeling the cumulative normal distribution, walk-forward calculation, and different ways to back-adjust futures. I haven't found any of these to be terribly helpful. I have setup a crude website on my PC:
http://toolkit.entonesoftware.com/Correlation/CorrOvODisplay.aspx
Correlation/cointegration is helpful in finding tradables with an economic relationship. The big question, though, is finding valid economic relationships which are being stressed but which are now being restored. (For example, electricity price vs a ceramic manufacturer. If the manufacturer is stressed too much, they will change to a different business.)
