Analysis of Stock Price Motion Asymmetry via Visibility-Graph Algorithm

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.

Comparing COVID-19 Incidences Longitudinally Per Economic Sector Against the Background of Preventive Measures and Vaccination

“…The proposed Gaussian–Gaussian model is generally applicable in settings where the goal is to compare aspects of asymmetrical curves such as height and timing of the peak, plateau phases, and speed of increase and decrease. Besides incidence, hospital admission and mortality due to COVID‐19 (Molenberghs et al., 2021; Nishimoto & Inoue, 2020), the Gaussian–Gaussian models may be applicable in the seasonal comparison of asymmetric growth‐curves of components of plants (Werker & Jaggard, 1997), quantification of tidal asymmetry (Guo et al., 2019), price and volume volatility (Liu & Chen, 2020), or studying hormonal homeostasis of circadian rhythms (Gnocchi & Bruscalupi, 2017). The data in each of those settings consist of (repeated) longitudinal asymmetric profiles with a similar general pattern.…”

A Bayesian analysis of gain-loss asymmetry

“…A similar analysis has been performed in Ref. [49], where the authors analyze the behavior of the market to investigate the rate of change in positive and negative price movements as a function of the time span. We compute the posterior distribution of the effect size d for both the proposed hierarchical models discussed in Section 2.…”

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

“…Here, we discriminate trajectories based on direction (rise or fall) as well as the shape (convex, concave, or otherwise). Note that the shape of a trajectory's geometry is difficult to define merely via statistical approaches because realized trajectories are the convolution of different temporal modes [31]. Hence, we keep employing the family of visibility algorithms; in the meantime, we also try to give a remedy to deficiencies of the VG-based or HVGbased method.…”