Abstract
Time irreversibility of a time series, which can be defined as the variance of properties under the time-reversal transformation, is a cardinal property of non-equilibrium systems and is associated with predictability in the study of financial time series. Recent pieces of literature have proposed the visibility-graph-based approaches that specifically refer to topological properties of the network mapped from a time series, with which one can quantify different degrees of time irreversibility within the sets of statistically time-asymmetric series. However, all these studies have inadequacies in capturing the time irreversibility of some important classes of time series. Here, we extend the visibility-graph-based method by introducing a degree vector associated with network nodes to represent the characteristic patterns of the index motion. The newly proposed method is parameter-free and temporally local. The validation to canonical synthetic time series, in the aspect of time (ir)reversibility, illustrates that our method can differentiate a non-Markovian additive random walk from an unbiased Markovian walk, as well as a GARCH time series from an unbiased multiplicative random walk. We further apply the method to the real-world financial time series and find that the price motions occasionally equip much higher time irreversibility than the calibrated GARCH model does.
Highlights
A time series with N scalar values, S {x1, . . . , xN}, is time-reversible if its properties are invariant under the time-reversal transformation [1, 2]
Time irreversibility is a fundamental property of nonequilibrium systems [3,4,5] and a dynamics that is under the influence of non-conservative forces [6]
How can we capture the topological properties of time series? Research Question 2
Summary
A time series with N scalar values, S {x1, . . . , xN}, is time-reversible if its properties are invariant under the time-reversal transformation [1, 2]. A time series with N scalar values, S {x1, . XN}, is time-reversible if its properties are invariant under the time-reversal transformation [1, 2]. X1} have identical properties, we can assert that the series is time-reversible. The time irreversibility of time series can be defined as the absence of time reversibility, i.e., S and St.r. have somewhat different properties. Since the source of the invariance between S and St.r. varies, it is natural to consider different degrees of time irreversibility within the sets of innately timeasymmetric time series such as those resulting from non-stationary, non-linear, or nonMarkovian processes [7]. The time (ir)reversibility of time series obtained in different domains have been investigated intensively because they provide rich information on the original dynamics
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have