JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (3): 41-48.doi: 10.6040/j.issn.1671-9352.0.2023.526

• Financial Mathematics • Previous Articles     Next Articles

Efficiency of stock index market based on improved recurrence plot

LIU Guidong1, KE Yilong2, YOU Guoqiao1*, LIU Manxi2   

  1. 1. School of Mathematics, Nanjing Audit University, Nanjing 211815, Jiangsu, China;
    2. School of Statistics and Data Science, Nanjing Audit University, Nanjing 211815, Jiangsu, China
  • Published:2025-03-10

PDF (PC)

30

Abstract: An enhanced computational model is introduced for the entropy based on recurrence microstates(ENRM), which builds upon the original method and employs an improved approach involving the traversal of submatrices using a rolling window. This improved computational model significantly improves computational efficiency while maintaining the accuracy of the original algorithm. For simulation experiments, a logistic model is employed, and the results prove that this improved computational model has higher computational efficiency and accuracy. Furthermore, research findings on market efficiency suggest that using the entropy based on recurrence microstates(ENRM)in combination with the traditional recurrence plot metric, entropy(ENTR), not only retains the ability of ENTR to quantify market efficiency but also effectively identifies and analyzes periods during which market efficiency undergoes dynamic evolution.

Key words: recurrence plot, entropy based on recurrence microstates, rolling window, market efficiency

CLC Number: 

  • O24
[1] LEKIEN F, LEONARD N. Dynamically consistent Lagrangian coherent structures[C] // Experimental Chaos: 8th Experimental Chaos Conference. Florence: AIP Publishing, 2004:132-139.
[2] SHADDEN S C, LEKIEN F, MARSDEN J E. Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows[J]. Physica D: Nonlinear Phenomena, 2005, 212:271-304.
[3] SAPSIS T, HALLER G. Inertial particle dynamics in a hurricane[J]. Journal of the Atmospheric Sciences, 2009, 66:2481-2492.
[4] CARDWELL B M, MOHSENI K. Vortex shedding over two-dimensional airfoil: where do the particles come from?[J]. AIAA Journal, 2008, 46(3):545-547.
[5] TANG W B, CHAN P W, HALLER G. Accurate extraction of Lagrangian coherent structures over finite domains with application to flight data analysis over Hong Kong International Airport[J]. Chaos, 2010, 20:017502.
[6] BADAS M G, DOMENICHINI F, QUERZOLI G. Quantification of the blood mixing in the left ventricle using finite time Lyapunov exponents[J]. Meccania, 2017, 52:529-544.
[7] LIPINSKI D, MOHSENI K. Flow structures and fluid transport for the hydromedusae Sarsia tubulosa and Aequorea victoria[J]. Journal of Experimental Biology, 2009, 212:2436-2447.
[8] GREEN M A, ROWLEY C W, SMITS A J. Using hyperbolic Lagrangian coherent structures to investigate vortices in bioinspired fluid flows[J]. Chaos, 2010, 20:017510.
[9] LUKENS S, YANG X Z, FAUCI L. Using Lagrangian coherent structures to analyze fluid mixing by cilia[J]. Chaos, 2010, 20:017511.
[10] MANDA B M, SENYANGE B, SKOKOS C. Chaotic wave-packet spreading in two-dimensional disordered nonlinear lattices[J]. Physical Review E, 2020, 101:032206.
[11] LASAGNA D, SHARMA A, MEYERS J. Periodic shadowing sensitivity analysis of chaotic systems[J]. Journal of Computational Physics, 2019, 391:119-141.
[12] CARUSONE A, SICOT C, BONNET J P. Transient dynamical effects induced by single-pulse fluidic actuation over an airfoil[J]. Experiments in Fluids, 2021, 62:25.
[13] ECKMANN J P, KAMPHORST S O, RUELLE D. Recurrence plots of dynamical systems[J]. Europhysics Letters, 1987, 4(9):973-977.
[14] 崔澜,张宏立,马萍,等. 基于递归熵及长短期记忆神经网络的滚动轴承退化趋势预测[J]. 轴承,2021,496(3):45-51,55. CUI Lan, ZHANG Hongli, MA Ping, et al. Prediction on degradation trend of rolling bearings based on recurrent entropy and long short-term memory neural network[J]. Bearing, 2021, 496(3):45-51,55.
[15] 尚前明,朱仁杰,杨安声,等. 基于RP-CNN的柴油机故障识别[J]. 船舶工程,2022,44(6):89-116. SHANG Qianming, ZHU Renjie, YANG Ansheng, et al. Fault identification of diesel engine based on RP-CNN[J]. Ship Engineering, 2022, 44(6):89-116.
[16] 钟季康,宋志怀,郝为强. RQA在肌电分析中的应用[J]. 生物物理学报,2002,18(2):241-245. ZHONG Jikang, SONG Zhihuai, HAO Weiqiang. Application of recurrence qualification analysis to emg[J]. Acta Biophysica Sinica, 2002, 18(2):241-245.
[17] WEBBER C L, ZBILUT J P. Dynamical assessment of physiological systems and states using recurrence plot strategies[J]. Journal of Applied Physiology, 1994, 76(2):965-973.
[18] MARWAN N, ROMANO M C, THIEL M, et al. Recurrence plots for the analysis of complex systems[J]. Physics Reports, 2007, 438(5/6):237-329.
[19] CORSO G, PRADO T L, LIMA G, et al. Quantifying entropy using recurrence matrix microstates[J]. Chaos, 2018, 28:083108.
[20] PRADO T L, CORSO G, LIMA G, et al. Maximum entropy principle in recurrence plot analysis on stochastic and chaotic systems[J]. Chaos, 2020, 30:043123.
[21] YOU Guoqiao, KE Yilong. ENRM: an alternative tool for studying dynamical systems[J]. Chaos, Solitons and Fractals, 2023, 174:113889.
[22] 吴礼斌,刘盛宇,王烨. 基于递归定量分析与内生结构突变模型的股票市场非线性特征研究[J]. 中国管理科学,2012,20:315-321. WU Libin, LIU Shengyu, WANG Ye. Using recurrence quantification analysis and endogenous structural break test to distinguish nonlinear dynamic characteristics of Chinas stock market[J]. Chinese Journal of Management Science, 2012, 20:315-321.
[23] 李燕,郝晓玲,李湛. 全球股市有效性的动态演化及量化比较研究[J]. 管理科学学报,2022,25(4):21-43. LI Yan, HAO Xiaoling, LI Zhan. Dynamic evolution and quantitative comparison of global stock market effectiveness[J]. Journal of Management Sciences in China, 2022, 25(4):21-43.
[24] 李燕. 基于递归图的股票市场非线性动力学演化研究[D]. 上海:上海财经大学,2020. LI Yan. Research on nonlinear dynamics evolution of stock market based on recurrence plot[D]. Shanghai: Shanghai University of Finance and Economics, 2020.
[1] Yuling LIU. Structured backward error for a class of generalized saddle point problems [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(10): 40-45.
[2] ALI Adil,RAHMAN Kaysar. Differential quadrature method for solving the generalized Burgers-Fisher equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(10): 30-39.
[3] Zhenai LI,Hui WEI,Xin CHEN. MNSGA-Ⅱ algorithm based on bi-objective for solving nonlinear equation systems [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(10): 22-29.
[4] Lulu AI,Yunxian LIU. An ultra-weak discontinuous Galerkin method for drift-diffusion model of semiconductor problem [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(10): 10-21.
[5] Yang WANG. Block triangular splitting and its preconditioning iterative algorithms for a class of complex symmetric linear systems [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(10): 1-9.
[6] Wenhui DU,Xiangtuan XIONG. Iterated fractional Tikhonov method for simultaneous inversion of the source term and initial data in time-fractional diffusion equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(8): 77-83.
[7] Xiumin LYU,Qian GE,Jin LI. Barycentric interpolation collocation method for solving the small-amplitude long-wave scheme generalized BBM-KdV equation [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(8): 67-76.
[8] ZHANG Ru, HAN Xu, LIU Xiao-gang. Convergence and contractivity of boundary value methods for nonlinear delay differential equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(8): 97-101.
[9] LI Cui-ping, GAO Xing-bao. A neural network for solving l1-norm problems with constraints [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(12): 90-98.
[10] CAO Wei-dong, DAI Tao, YU Jin-biao, WANG Xiao-hong, SHI An-feng. Improvement on the solution of pressure equation based on alternating direction in chemical flooding model [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(10): 88-94.
[11] DING Feng-xia, CHENG Hao. A posteriori choice rule for the mollification regularization parameter for the Cauchy problem of an elliptic equation [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(2): 18-24.
[12] . Interval algorithm for mixed integer nonlinear two-level programming problems [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(2): 9-17.
[13] KONG Yi-ting, WANG Tong-ke. The steepest descent method for Fourier integrals involving algebraic and logarithmic singular factors [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(10): 50-55.
[14] YU Jin-biao, REN Yong-qiang, CAO Wei-dong, LU Tong-chao, CHENG Ai-jie, DAI tao. Expanded mixed finite element method for compressible miscible displacement in heterogeneous porous media [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(8): 25-34.
[15] SHI Zhang-lei, LI Wei-guo. A† graded hard thresholding pursuit algorithm [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(8): 58-64.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] WANG Bing . Properties of a quasi-claw-free graph[J]. J4, 2007, 42(10): 111 -113 .
[2] ZHU yan,HOU Jian-feng,WANG Ji-hui . [J]. J4, 2006, 41(5): 59 -62 .
[3] Ming-Chit Liu. THE TWO GOLDBACH CONJECTURES[J]. J4, 2013, 48(2): 1 -14 .
[4] WANG Kai-rong, GAO Pei-ting. Two mixed conjugate gradient methods based on DY[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(6): 16 -23 .
[5] WU Dai-yong, ZHANG Hai. Stability and bifurcation analysis for a single population discrete model with Allee effect and delay[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(07): 88 -94 .
[6] . [J]. J4, 2009, 44(3): 84 -87 .
[7] GUO Lei,YU Rui-lin and TIAN Fa-zhong . Optimal control of one kind general jump transition systems[J]. J4, 2006, 41(1): 35 -40 .
[8] YANG Lun, XU Zheng-gang, WANG Hui*, CHEN Qi-mei, CHEN Wei, HU Yan-xia, SHI Yuan, ZHU Hong-lei, ZENG Yong-qing*. Silence of PID1 gene expression using RNA interference in C2C12 cell line[J]. J4, 2013, 48(1): 36 -42 .
[9] LIU Yan-ping, WU Qun-ying. Almost sure limit theorems for the maximum of Gaussian sequences#br# with optimized weight[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(05): 50 -53 .
[10] DU Ji-xiang1,2, YU Qing1, ZHAI Chuan-ming1. Age estimation of facial images based on non-negative matrix factorization with sparseness constraints[J]. J4, 2010, 45(7): 65 -69 .
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd