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.

本文是第一篇通过将可见度图和不可见度图算法应用于股票指数分析来区分凹凸价格运动轨迹的方法。引入了用于价格上涨和下跌运动的凹凸指标来表征加速和减速的股指的上涨和下跌。通过比较这些指标的分布，可以发现价格运动轨迹中存在不对称性，并且以时间和指标变化之间的Kullback-Leibler差异为特征的不对称度会在时间范围变化后波动。 。此外，通过比较节点的可见度和不可见度图上的条件预期上升和下降收益，可以证明价格运动速度的不对称性。