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

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

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.

Highlights

This paper is based on the famous log-periodic power law model
in financial physics to warn of the collapse of China's Shanghai Composite Index
In view of the existing research using the log-periodic power law model (LPPL) model to warn of market crash

Summary

LPPL 模型介绍

LPPL 模型进行刻画. LPPL 模型具有如下特性: s 1) 投资者之间相互模仿, 呈现集体追涨的交 s 易局面, 造成对数资产价格呈超指数暴涨; e 2) 随着资产价格泡沫破裂的风险逐渐扩大, r 市场需要更高的回报作为补偿; 3) 资产价格泡沫在临界点 tc 具有最大的崩盘 h (t)) dt = h (t) dt . 价增长的加速度, m 越小, 股价增长的加速度越快, 其临近泡沫的可能性也越大. w 为振荡的角频率, f 为振荡的初始相位. dp Et p = κh (t) dt. 顶时的价格; B = −κB′/m ; C = −κC′/ m2 + ω2 . 并且, B(tc − t)m 反映了股价由正反馈机制驱使而出现的幂律增长特性, C(tc − t)m cos(ω ln(tc − t) − φ) 模型中呈现的对数周期幂律振荡现象. 图 1 上证指数 2015 年泡沫期间 LPPL 拟合图 Fig. 1. LPPL fitting diagram of the Shanghai stock exchange (SSE) index during the 2015 bubble. ln(67) = ln(67)–ln(38) = ln(38)–ln(22) = ln(22)– ln(13) = 0.54. 并且股价越是接近临界点, 股价增长速度越快, 即股价增长率呈现单调递增的特点.

LPPL-MS 模型的构建

LPPL-MS 拟合结果及分析