>nad, I think it is delibrate: they don’t want to use future data (which won’t be known when making a prediction). Fig 4 in the supplemetary info shows a typical result.

Do you mean that they write:
> representative example of the absolute value of the cross-correlation function

but mean the cross-covariance?

I guess thats rather clearly just a typo. Unfortunately I am not so sure
though in the above formula for the cross covariance wether this is a typo. It might be that they used what looks to me like "another" form of
correlation. Whatever this means for the result.