We propose a statistical resampling scheme that generates an ensemble of permuted time series by repeatedly swapping randomly selected pairs of adjacent data points. In the infinite ensemble limit, we derive the exact ensemble-average operator, which describes how the ensemble average evolves with the number of swaps and satisfies a discrete diffusion equation. Under a periodic idealization, the corresponding transfer function reduces asymptotically to the Gaussian response in the low frequency limit when the number of swaps is on the order of the data length. The ensemble-average operator also affords a dimensionless relation involving the residue between the original and ensemble-averaged time series, the magnitude of the first difference, the number of swaps, and the data length. When the time series is dominated by white noise, this relation reduces to a similarity function that depends solely on the normalized number of swaps. This result motivates a procedure based on the Kolmogorov–Smirnov test for selecting the extent of permutation according to approximate preservation of the marginal first-difference distribution. Under the periodic idealization, the characteristic function of the random displacement of an individual data value is identical to the transfer function of the ensemble-average operator, thereby providing a destructive interference interpretation of the operator’s low-pass behavior. Finally, the individual permuted time series are demonstrated as surrogate inputs to downstream analyses in a proof of concept application using empirical mode decomposition.