How to normalize Futures data(different leverage) for cointegration test?

For example I want to construct 2 time series, one for ES and the other for NQ and test for cointegration.

ES one point equal to 50$. NQ one point equal to 20$.

If I have the following data:

ES[0]=1300;ES[1]=1307;ES[2]=1314...

NQ[0]=2700;NQ[1]=2692;NQ[2]=2715...

How do I normalize this data for cointegration test?

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Multiply each price series by its multiplier to get notional values. Then proceed as if the notional value were the price of 1 share.

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It sounds like you want to look at constant volatility series. Just divide the returns by some volatility measure on each series respectively (e.g. ($r_t * volatilitytarget)/\sigma(50 days)$). Then the change in one will be equivalent in size to the change in the other.

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