Time irreversibility of financial time series based on higher moments and multiscale Kullback–Leibler divergence

2018 ◽  
Vol 502 ◽  
pp. 248-255 ◽  
Author(s):  
Jinyang Li ◽  
Pengjian Shang
Keyword(s):  
Time Series ◽  
Financial Time Series ◽  
Higher Moments ◽  
Financial Time ◽  
Leibler Divergence ◽  
Time Irreversibility

scholarly journals Measuring the Topological Time Irreversibility of Time Series With the Degree-Vector-Based Visibility Graph Method

2021 ◽  
Vol 9 ◽  
Author(s):  
Ryutaro Mori ◽  
Ruiyun Liu ◽  
Yu Chen
Keyword(s):  
Time Series ◽  
Random Walk ◽  
Time Reversal ◽  
Financial Time Series ◽  
Visibility Graph ◽  
Topological Properties ◽  
Network Nodes ◽  
Financial Time ◽  
Time Irreversibility ◽  
Synthetic Time Series

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.

Jensen–Shannon Divergence Based on Horizontal Visibility Graph for Complex Time Series

2020 ◽  
pp. 2150013
Author(s):  
Yi Yin ◽  
Wenjing Wang ◽  
Qiang Li ◽  
Zunsong Ren ◽  
Pengjian Shang
Keyword(s):  
Time Series ◽  
Financial Time Series ◽  
Visibility Graph ◽  
Horizontal Visibility ◽  
Stock Indices ◽  
Leibler Divergence ◽  
Time Irreversibility ◽  
Jensen Shannon Divergence ◽  
Time Series Irreversibility ◽  
Horizontal Visibility Graph

In this paper, we propose Jensen–Shannon divergence (JSD) based on horizontal visibility graph (HVG) to measure the time series irreversibility for both stationary and non-stationary series efficiently. Numerical simulations are first conducted to show the validity of the proposed method and then empirical applications to the financial time series and traffic time series are investigated. It can be found that JSD shows better robustness than Kullback–Leibler divergence (KLD) on quantifying time series irreversibility and correctly distinguishes the different type of simulated series. For the empirical analysis, JSD based on HVG is able to detect the significant time irreversibility of stock indices and reveal the relationship between different stock indices. JSD results show the time irreversibility of speed time series for different detectors and present better accuracy and robustness than KLD. The hierarchical clustering based on their behavior of time irreversibility obtained by JSD classifies the detectors into four groups.

EMPIRICAL TESTING OF MULTIFRACTALITY OF FINANCIAL TIME SERIES BASED ON WTMM

Fractals ◽  
2009 ◽  
Vol 17 (03) ◽  
pp. 323-332 ◽  
Author(s):  
ROSSITSA YALAMOVA
Keyword(s):  
Time Series ◽  
Financial Time Series ◽  
Applied Mathematics ◽  
Multifractal Spectrum ◽  
Higher Moments ◽  
Market Returns ◽  
Financial Time ◽  
Wavelet Transform Modulus Maxima ◽  
Modulus Maxima ◽  
Mathematics And Physics

The multifractal spectrum calculated with wavelet transform modulus maxima (WTMM) provides information on the higher moments of market returns distribution and the multiplicative cascade of volatilities. This paper applies a wavelet based methodology for calculation of the multifractal spectrum of financial time series. WTMM methodology provides a better measure of risk changes compared to the structure function approach. It is well founded in applied mathematics and physics with little popularity among finance researchers.

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