Constrained Markov order surrogates

Débora Cristina Corrêa, Jack Murdoch Moore, Thomas Jüngling, Michael Small

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


We describe a surrogates algorithm for symbolic time series which consists of constrained permutation of strings and exactly preserves the nth-order Markov properties of the original data. In the context of hypothesis tests, each surrogate generated by the algorithm provides another realisation of the same Markov process posited in the null hypothesis. We prove uniformity, convergence and range, and validate numerically the properties of the algorithm with traditional hypothesis tests. Finally we apply it to real-world data from U.S. business cycles. The swapping algorithm can also be interpreted as a constrained realisation of a random walk in a network.

Original languageEnglish
Article number132437
JournalPhysica D: Nonlinear Phenomena
Publication statusPublished - 1 May 2020


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