We show that traditional Reynolds (block) averaging produces turbulence statistics whose time evolution is incompatible with the Navier–Stokes equation. Specifically, the zero integral scale that block averaging always produces leads to a trivial (zero-equals-zero) solution of the Navier–Stokes equation for autocovariances. We suggest alternative methods for analyzing turbulence time series that do not always generate a zero integral scale and, as a result, yield autocovariances whose time evolutions are compatible with the Navier–Stokes equation.