Research on Chinese stock market crash early warning based on improved log-periodic power law model

Wu Jun-Chuan; Tang Zhen-Peng; Du Xiao-Xu; Chen Kai-Jie

doi:10.7498/aps.71.20201940

Abstract

This paper is based on the famous log-periodic power law model (LPPL) in financial physics to warn of the collapse of China's Shanghai Composite Index and GEM Index in June 2015. In view of the existing research using the LPPL model to warn of market crash, only the historical trading data of the market are considered. For the first time, investor sentiment factors are incorporated into the modeling process of LPPL model to improve the early warning effect of LPPL model. Using the text mining technology combined with semantic analysis methods to grasp the financial media's stock evaluation report for word frequency statistics, in order to build the medium sentiment index. The further modified expression of the crash probability function in the LPPL model is represented as a function of historical trading data and medium sentiment, and thus constructing an LPPL-MS combination model to warn of stock market crash. The empirical results show that the LPPL-MS combination model constructed in this paper has higher warning accuracy than the LPL model, and its prediction crash time is closer to the actual crash time of the Shanghai Index and GEM Index, and its fitting results have passed the relevant test.

Keywords:

Authors and contacts

School of Economics and Management, Fuzhou University, Fuzhou 350108, China

Corresponding author: Tang Zhen-Peng, zhenpt@126.com

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 71573042, 71973028)

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References

[1]	Sornette D, Johansen A, Bouchaud J P 1995 J. Phys. I. 6 167 Google Scholar
[2]	Johansen A, Sornette D 1999 Risk. 12 91
[3]	Jensen M C 1967 Financ. Anal. J. 23 77
[4]	Fama U 1965 J. Bus. 38 34 Google Scholar
[5]	蒋志强, 田婧雯, 周炜星 2019 管理科学学报 22 92 Google Scholar Jiang Z Q, Tian J W, Zhou W X 2019 J. Manag. Sci. China 22 92 Google Scholar
[6]	徐翔, 朱承, 朱先强 2021 70 088901 Google Scholar Xu X, Zhu C, Zhu X Q 2021 Acta Phys. 70 088901 Google Scholar
[7]	Gurkaynak R S 2008 J. Econ. Sury. 22 166 Google Scholar
[8]	Bak P, Tang C, Wiesenfeld K 1987 Phys. Rev. Lett. 59 381 Google Scholar
[9]	潘娜, 王子剑, 周勇 2018 中国管理科学 26 25 Google Scholar Pan N, Wang Z J, Zhou Y 2018 Chin. J. Manag. Sci. 26 25 Google Scholar
[10]	周炜星 2007 金融物理学导论 (上海: 上海财经大学出版社) 第17—33页 Zhou W X 2007 Introduction of Econophysics (Shang-hai: Shanghai University of Finance and Economics Press) pp17–33 (in Chinese)
[11]	Sornette D, Johansen A 1997 Physica A 245 411 Google Scholar
[12]	Sornette D, Johansen A 1998 Physica A 261 581 Google Scholar
[13]	Sornette D, Zhou W X 2006 Int. J. Forecast 22 153 Google Scholar
[14]	Sornette D, Woodard R, Zhou W X 2009 Physica A 388 1571 Google Scholar
[15]	Kyriazis N, Papadamou S, Corbet S 2020 Res. Int. Bus. Financ. 54 101254 Google Scholar
[16]	Omer O 2020 Eur. Phys. J. Spec. Top. 229 1715 Google Scholar
[17]	Sirca S J, Omladic M 2020 ARS Math. Contemp. 13 63
[18]	Filimonov V, Sornette D 2013 Physica A 392 3698 Google Scholar
[19]	Jiang Z, Zhou W X, Sornette D, et al. 2010 J. Econ. Behav. Organ. 74 149 Google Scholar
[20]	Yan W, Rebib R, Woodard R, Sornette D 2012 IJPAM. 1 59 Google Scholar
[21]	李东 2012 淮海工学院学报(自然科学版) 21 4 Li D 2012 J. Huaihai Insti of Tech. (Natural Science Edition) 21 4
[22]	周伟, 何建敏 2011 金融研究 375 65 Zhou W, He J M 2011 J. Financ. Res. 375 65
[23]	李斯嘉, 李冬昕, 王粟旸 2017 上海经济研究 7 42 Li S J, Li D X, Wang L Y 2017 Shanghai J. Econ. 7 42
[24]	李伦一, 张翔 2019 金融研究 474 169 Li L Y, Zhang X 2019 J. Financ. Res. 474 169
[25]	陈卫华, 蔡文靖 2018 统计与决策 497 143 Google Scholar Chen W H, Cai W J 2018 Statistics and Decision 497 143 Google Scholar
[26]	赵磊, 刘庆 2020 统计与决策 558 128 Google Scholar Zhao L, Liu Q 2020 Statistics and Decision 558 128 Google Scholar
[27]	Kahneman D 2003 Am. Econ. Rev. 93 1449 Google Scholar
[28]	Baker M, Wurgler J 2006 J. Financ. 61 1645 Google Scholar
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[33]	Solomon D H 2012 J. Financ. 67 599 Google Scholar
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[35]	Fisher K L, Statman M 2000 Financ. Anal. J. 56 16 Google Scholar
[36]	武佳薇, 汪昌云, 陈紫琳, Jie Michael Guo 2020 金融研究 476 147 Wu J W, Wang C Y, Chen Z L, Jie M G 2020 J. Financ. Res. 476 147
[37]	李合龙, 冯春娥 2014 系统工程理论与实践 34 2495 Google Scholar Li H L, Feng C E 2014 System Eng. Theor. Prac. 34 2495 Google Scholar
[38]	游家兴, 吴静 2012 经济研究 534 141 You J X, Wu J 2012 Econ. Res. J 534 141
[39]	Wu D D, Zheng L, Olson D L 2014 IEEE T. SYST Man CY-S. 44 1077 Google Scholar
[40]	戴德宝, 兰玉森, 范体军, 赵敏 2019 中国软科学 340 166 Google Scholar Dai D B, Lan Y S, Fan T J, Zhao M 2019 China Soft Sci. 340 166 Google Scholar
[41]	Martin G 1971 In Computers, Communication, and the Public Interest (Baltimore, MD: The Johns Hopkins Press) p37
[42]	Da Z, Engelberg J, Gao P 2011 J. Financ. 66 1461 Google Scholar
[43]	Huang X, Nekrasov A, Teoh S H 2018 Account. Rev. 93 231 Google Scholar
[44]	Sentiment Analysis, Bian S B, Jia D K, Li F http://dx.doi.org/10.2139/ssrn.3446388 [2020-11-10]
[45]	王晓丹, 尚维, 汪寿阳 2019 系统工程理论与实践 39 3038 Google Scholar Wang X D, Shang W, Wang S Y 2019 System Eng. Theor. Prac. 39 3038 Google Scholar
[46]	Johansen A, Ledoit O, Sornette D. 2000 Int J Theor Appl Finan. 3 219 Google Scholar
[47]	Yan W F, Woodard R, Sornette D 2014 Quant. Financ. 14 1273 Google Scholar
[48]	Lin L, Sornette D 2013 Eur. J. Financ. 19 344 Google Scholar

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图 1 上证指数2015年泡沫期间LPPL拟合图

Figure 1. LPPL fitting diagram of the Shanghai stock exchange (SSE) index during the 2015 bubble.

DownLoad: Full-Size Img PowerPoint

图 2 部分财经媒体评论稿标题信息样本

Figure 2. Some financial media commentary title information samples.

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图 3 上证指数、创业板指数泡沫前后走势

Figure 3. Trend of SSE index and growth enterprise market (GEM) index before and after bubble.

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图 4 上证指数、创业板指数不同模型预测表现比较分析

Figure 4. Comparative analysis of forecasting performance of different models of Shanghai Stock Exchange Index and Growth Enterprise Market Index.

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表 1 CFSD词典部分积极、消极词汇

Table 1. Some positive and negative words in CFSD dictionary.

序号	积极词汇	消极词汇
1	突破	拖累
2	增长	不涨反跌
3	高涨	分化
4	火爆	沉重打击
5	赚钱	恐慌
6	上升	下降
7	一枝独秀	狂跌
8	蒸蒸日上	跌停板
9	活跃	退市
10	提速	暴涨暴跌

DownLoad: CSV

表 2 (MS)序列描述性统计分析

Table 2. Descriptive statistical analysis of media sentiment(MS) sequence.

最大值	最小值	均值	标准差	偏度	峰度
1.794	–0.998	0.252	0.446	0.037	3.158

DownLoad: CSV

表 3 上证指数LPPL, LPPL-MS参数估计结果

Table 3. Parameter estimation results of SSE index LPPL and LPPL-MS.

	MSE	A	B	C	m	ω	ϕ	λ	$ {t_{\text{c}}} $
LPPL	0.997	10.131	–0.864	–0.017	0.188	12.098	1.748	—	369.022
	1.078	10.161	–0.828	–0.015	0.197	11.991	1.840	—	379.036
	1.112	9.949	–0.805	0.014	0.188	10.368	2.029	—	361.668
LPPL-MS	0.948	9.639	–0.562	–0.014	0.226	12.398	6.686	0.008	362.729
	0.991	9.597	–0.509	–0.013	0.240	12.911	3.717	0.007	365.669
	1.038	9.552	–0.508	–0.012	0.237	12.953	3.671	0.010	360.949

DownLoad: CSV

表 4 创业板指数LPPL、LPPL-MS参数估计结果

Table 4. Estimation results of LPPL and LPPL-MS parameters of gem index.

	MSE	A	B	C	m	ω	ϕ	λ	$ {t_{\text{c}}} $
LPPL	2.429	8.444	–0.334	0.006	0.239	13.988	2.241	—	335.923
	2.443	8.654	–0.436	–0.015	0.217	13.009	3.989	—	341.826
	2.477	8.517	–0.355	–0.011	0.236	13.039	3.998	—	340.435
LPPL-MS	2.703	8.617	–0.395	0.011	0.229	15.242	0.288	0.015	344.122
	2.819	9.218	–0.766	0.016	0.174	16.445	5.320	0.010	352.216
	2.904	8.922	–0.559	0.010	0.200	21.717	0.256	0.010	353.759

DownLoad: CSV

表 5 上证指数、创业板指数预警误差比较分析

Table 5. Comparative analysis of early warning errors between SSE index and GEM index.

		最低绝对误差	最高绝对误差	平均绝对误差
LPPL	上证指数	9	27	18
LPPL	创业板指	4	10	7
LPPL-MS	上证指数	8^*	13^*	11^*
LPPL-MS	创业板指	1^*	8^*	6^*
注: *表明预测的见顶时点最接近真实值.

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表 6 上证指数、创业板指数不同拟合情形下残差平稳性检验

Table 6. Residual stationarity test of SSE index and GEM index under different fitting conditions.

		拟合情形1	拟合情形2	拟合情形3
LPPL	上证指数	0.014^**	0.021^**	0.013^**
LPPL	创业板指	0.0428^**	0.073^*	0.0959^*
LPPL-MS	上证指数	0.001^***	0.001^***	0.012^**
LPPL-MS	创业板指	0.019^**	0.041^**	0.074^*
注: 表明在10%水平下显著; 表明在5%水平下显著; **表明在1%水平下显著.

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[1]	Sornette D, Johansen A, Bouchaud J P 1995 J. Phys. I. 6 167 Google Scholar
[2]	Johansen A, Sornette D 1999 Risk. 12 91
[3]	Jensen M C 1967 Financ. Anal. J. 23 77
[4]	Fama U 1965 J. Bus. 38 34 Google Scholar
[5]	蒋志强, 田婧雯, 周炜星 2019 管理科学学报 22 92 Google Scholar Jiang Z Q, Tian J W, Zhou W X 2019 J. Manag. Sci. China 22 92 Google Scholar
[6]	徐翔, 朱承, 朱先强 2021 70 088901 Google Scholar Xu X, Zhu C, Zhu X Q 2021 Acta Phys. 70 088901 Google Scholar
[7]	Gurkaynak R S 2008 J. Econ. Sury. 22 166 Google Scholar
[8]	Bak P, Tang C, Wiesenfeld K 1987 Phys. Rev. Lett. 59 381 Google Scholar
[9]	潘娜, 王子剑, 周勇 2018 中国管理科学 26 25 Google Scholar Pan N, Wang Z J, Zhou Y 2018 Chin. J. Manag. Sci. 26 25 Google Scholar
[10]	周炜星 2007 金融物理学导论 (上海: 上海财经大学出版社) 第17—33页 Zhou W X 2007 Introduction of Econophysics (Shang-hai: Shanghai University of Finance and Economics Press) pp17–33 (in Chinese)
[11]	Sornette D, Johansen A 1997 Physica A 245 411 Google Scholar
[12]	Sornette D, Johansen A 1998 Physica A 261 581 Google Scholar
[13]	Sornette D, Zhou W X 2006 Int. J. Forecast 22 153 Google Scholar
[14]	Sornette D, Woodard R, Zhou W X 2009 Physica A 388 1571 Google Scholar
[15]	Kyriazis N, Papadamou S, Corbet S 2020 Res. Int. Bus. Financ. 54 101254 Google Scholar
[16]	Omer O 2020 Eur. Phys. J. Spec. Top. 229 1715 Google Scholar
[17]	Sirca S J, Omladic M 2020 ARS Math. Contemp. 13 63
[18]	Filimonov V, Sornette D 2013 Physica A 392 3698 Google Scholar
[19]	Jiang Z, Zhou W X, Sornette D, et al. 2010 J. Econ. Behav. Organ. 74 149 Google Scholar
[20]	Yan W, Rebib R, Woodard R, Sornette D 2012 IJPAM. 1 59 Google Scholar
[21]	李东 2012 淮海工学院学报(自然科学版) 21 4 Li D 2012 J. Huaihai Insti of Tech. (Natural Science Edition) 21 4
[22]	周伟, 何建敏 2011 金融研究 375 65 Zhou W, He J M 2011 J. Financ. Res. 375 65
[23]	李斯嘉, 李冬昕, 王粟旸 2017 上海经济研究 7 42 Li S J, Li D X, Wang L Y 2017 Shanghai J. Econ. 7 42
[24]	李伦一, 张翔 2019 金融研究 474 169 Li L Y, Zhang X 2019 J. Financ. Res. 474 169
[25]	陈卫华, 蔡文靖 2018 统计与决策 497 143 Google Scholar Chen W H, Cai W J 2018 Statistics and Decision 497 143 Google Scholar
[26]	赵磊, 刘庆 2020 统计与决策 558 128 Google Scholar Zhao L, Liu Q 2020 Statistics and Decision 558 128 Google Scholar
[27]	Kahneman D 2003 Am. Econ. Rev. 93 1449 Google Scholar
[28]	Baker M, Wurgler J 2006 J. Financ. 61 1645 Google Scholar
[29]	Baker M, Wurgler J 2007 J. Econ. Perspect 21 129 Google Scholar
[30]	García D 2013 J. Financ. 68 1267 Google Scholar
[31]	Fang L, Peress J 2009 J. Financ. 64 2023 Google Scholar
[32]	Barber B M, Odean T 2008 Rev. Financ. Stud. 21 785 Google Scholar
[33]	Solomon D H 2012 J. Financ. 67 599 Google Scholar
[34]	Nardo M, Petracco-Giudici M, Naltsidis M 2016 J. Econ. Surv. 30 356 Google Scholar
[35]	Fisher K L, Statman M 2000 Financ. Anal. J. 56 16 Google Scholar
[36]	武佳薇, 汪昌云, 陈紫琳, Jie Michael Guo 2020 金融研究 476 147 Wu J W, Wang C Y, Chen Z L, Jie M G 2020 J. Financ. Res. 476 147
[37]	李合龙, 冯春娥 2014 系统工程理论与实践 34 2495 Google Scholar Li H L, Feng C E 2014 System Eng. Theor. Prac. 34 2495 Google Scholar
[38]	游家兴, 吴静 2012 经济研究 534 141 You J X, Wu J 2012 Econ. Res. J 534 141
[39]	Wu D D, Zheng L, Olson D L 2014 IEEE T. SYST Man CY-S. 44 1077 Google Scholar
[40]	戴德宝, 兰玉森, 范体军, 赵敏 2019 中国软科学 340 166 Google Scholar Dai D B, Lan Y S, Fan T J, Zhao M 2019 China Soft Sci. 340 166 Google Scholar
[41]	Martin G 1971 In Computers, Communication, and the Public Interest (Baltimore, MD: The Johns Hopkins Press) p37
[42]	Da Z, Engelberg J, Gao P 2011 J. Financ. 66 1461 Google Scholar
[43]	Huang X, Nekrasov A, Teoh S H 2018 Account. Rev. 93 231 Google Scholar
[44]	Sentiment Analysis, Bian S B, Jia D K, Li F http://dx.doi.org/10.2139/ssrn.3446388 [2020-11-10]
[45]	王晓丹, 尚维, 汪寿阳 2019 系统工程理论与实践 39 3038 Google Scholar Wang X D, Shang W, Wang S Y 2019 System Eng. Theor. Prac. 39 3038 Google Scholar
[46]	Johansen A, Ledoit O, Sornette D. 2000 Int J Theor Appl Finan. 3 219 Google Scholar
[47]	Yan W F, Woodard R, Sornette D 2014 Quant. Financ. 14 1273 Google Scholar
[48]	Lin L, Sornette D 2013 Eur. J. Financ. 19 344 Google Scholar

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