Unnormalized time autocorrelation (source code)

= Unnormalized time autocorrelation
{title2=$C(t,\tau)=\langle X(t)X(t+\tau)\rangle$}

The raw same-observable time correlation $C(t,\tau)=\langle X(t)X(t+\tau)\rangle$. For a <Stationary process> with finite <second moment>[second moments], it equals $\langle X\rangle^2+\operatorname{Cov}(X(t),X(t+\tau))$. Its connected part is the <autocovariance>; unlike the normalized statistical <autocorrelation>, no division by the <variance> is imposed. The distinction matters for fluctuations around a nonzero <equilibrium point>.