I want to use the Monte Carlo Method described in Aronsons book Evidence based Technical Analysis to test if a given pairs trading strategy is useless.
First step there is to randomize the returns of the underlying instrument. Second step is to calculate daily log returns of the strategy as a performence measure.

For the first step: Is it sufficient to randomize the spread that is already calculated or are the underlying instruments to be randomized and hedging coefficient estimation to be repeated?

For the second step: log returns for spreads are not suitable since the spread can have negative values. So may be better use differencies of spread today minus spread yesterday?