transvers current correlation function (MD)

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I am trying to calculate some hydrodynamic properties from MD results. Part of the process in to calculate the transvers current correlation function which is formulated as $C(q,t)=\langle J^*(0)J(t) \rangle$. The issue is that this formula is regarded as canonical ensemble average in literature which should be calculated based on parameter $\Beta$. However my intuition is that this should be a form of autocorrelation or cross correlation of a rolling window. This is confusing to me and I would like to ask if anyone can provide me a pseudo code example for this calculation.