Antipersistent binary time series

Abstract

Completely antipersistent binary time series are sequences in which every time that an $N$-bit string $\mu$ appears, the sequence is continued with a different bit than at the last occurrence of $\mu$. This dynamics is phrased in terms of a walk on a DeBruijn graph, and properties of transients and cycles are studied. The predictability of the generated time series for an observer who sees a longer or shorter time window is investigated also for sequences that are not completely antipersistent.