# 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?

-

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

-

In a co-integration test you rely on the original price series -- not transformations of the price series such as rate of change and so on. Seems to me there is no need for normalization.

-
A "normalization" can be a useful nonlinear transformation quite different from differencing (which should be generally avoided, as you suggest - unless one is dealing with higher order cointegration). –  Ryogi Oct 27 '11 at 22:08
excellent point –  Quant Guy Oct 28 '11 at 4:23
but my problem quantGuy is that if you want to trade such a portfolio the different leverage of each instrument is not taken into account.What I think should be done is multiply the price by the point value and then look for cointegration. Does it make sense to you? –  Freewind Oct 28 '11 at 8:39
I see. Yes, that makes sense. Your assumption is that the notional value per @user508's point is stationary. You test for cointegration after adjusting for leverage. –  Quant Guy Oct 28 '11 at 15:28

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.

-