%0 Generic %1 Lacasa2015Time %A Lacasa, Lucas %A Flanagan, Ryan %D 2015 %K statistics %T Time reversibility from visibility graphs of non-stationary processes %U http://arxiv.org/abs/1510.01318 %X Visibility algorithms are a family of methods to map time series into networks, with the aim of describing the structure of time series and their underlying dynamical properties in graph-theoretical terms. Here we explore some properties of both natural and horizontal visibility graphs associated to several non-stationary processes, and we pay particular attention to their capacity to assess time irreversibility. Non-stationary signals are (infinitely) irreversible by definition (independently of whether the process is Markovian or producing entropy at a positive rate), and thus the link between entropy production and time series irreversibility has only been explored in non-equilibrium stationary states. Here we show that the visibility formalism naturally induces a new working definition of time irreversibility, which allows to quantify several degrees of irreversibility for stationary and non-stationary series, yielding finite values that can be used to efficiently assess the presence of memory and off-equilibrium dynamics in non-stationary processes without needs to differentiate or detrend them. We provide rigorous results complemented by extensive numerical simulations on several classes of stochastic processes.

@misc{Lacasa2015Time, abstract = {{Visibility algorithms are a family of methods to map time series into networks, with the aim of describing the structure of time series and their underlying dynamical properties in graph-theoretical terms. Here we explore some properties of both natural and horizontal visibility graphs associated to several non-stationary processes, and we pay particular attention to their capacity to assess time irreversibility. Non-stationary signals are (infinitely) irreversible by definition (independently of whether the process is Markovian or producing entropy at a positive rate), and thus the link between entropy production and time series irreversibility has only been explored in non-equilibrium stationary states. Here we show that the visibility formalism naturally induces a new working definition of time irreversibility, which allows to quantify several degrees of irreversibility for stationary and non-stationary series, yielding finite values that can be used to efficiently assess the presence of memory and off-equilibrium dynamics in non-stationary processes without needs to differentiate or detrend them. We provide rigorous results complemented by extensive numerical simulations on several classes of stochastic processes.}}, added-at = {2019-02-23T22:09:48.000+0100}, archiveprefix = {arXiv}, author = {Lacasa, Lucas and Flanagan, Ryan}, biburl = {https://www.bibsonomy.org/bibtex/2b7e74ba72835e30937ca3ad5314edddb/cmcneile}, citeulike-article-id = {13796897}, citeulike-linkout-0 = {http://arxiv.org/abs/1510.01318}, citeulike-linkout-1 = {http://arxiv.org/pdf/1510.01318}, day = 5, eprint = {1510.01318}, interhash = {4e8678bf64c4165465e6a30a0f4d22a7}, intrahash = {b7e74ba72835e30937ca3ad5314edddb}, keywords = {statistics}, month = oct, posted-at = {2015-10-07 13:26:58}, priority = {2}, timestamp = {2019-02-23T22:15:27.000+0100}, title = {{Time reversibility from visibility graphs of non-stationary processes}}, url = {http://arxiv.org/abs/1510.01318}, year = 2015 }