Abstract
This paper is the first to differentiate between concave and convex price motion trajectories by applying visibility-graph and invisibility-graph algorithms to the analyses of stock indices. Concave and convex indicators for price increase and decrease motions are introduced to characterize accelerated and decelerated stock index increases and decreases. Upon comparing the distributions of these indicators, it is found that asymmetry exists in price motion trajectories and that the degree of asymmetry, which is characterized by the Kullback-Leibler divergence between the distributions of rise and fall indictors, fluctuates after a change in time scope. Moreover, asymmetry in price motion speeds is demonstrated by comparing conditional expected rise and fall returns on the node degrees of visibility and invisibility graphs.
Highlights
The use of network science to perform time series analysis has emerged in recent decades
We propose to study the financial time series asymmetry via visibility-graph networks based on the intuition that network approaches may be more effective in identifying different price motion trajectories
Graph networks for accelerated or decelerated rise (AR) and DF motions of a stock index can be constructed by mapping a time series of length L, X(ti)(i < L) onto a graph network using visibilitygraph algorithm (VGA)
Summary
The use of network science to perform time series analysis has emerged in recent decades. It is worth mentioning that conventional VGA analysis cannot be applied directly to investigation of the topologically asymmetric properties of financial series because the method is incapable of distinguishing different stock price rise and fall trajectories by mapping the time series as a whole onto an undirected network. To solve this problem, an idea from Yan et al (2012) [43] is borrowed to address discrimination between price movements via visibility and invisibility-graph (IVG) networks.
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