Abstract：Different from the previous studies on the long memory and effectiveness of stock market returns and volatility, this paper focuses on the extreme fluctuation behavior of financial markets. Taking the most representative index of Chinese stock market, Shanghai stock index, as the sample, the financial market is divided into different time windows according to a certain period, and the extreme returns in each time window are formed into a time series. Taking extreme return series as the empirical research object, this paper studies the long memory of extreme return in Shanghai stock market by using multiple statistical methods such as rescaling range analysis and Detrended fluctuation analysis. The results show that both extreme return series and extreme volatility series have obvious long memory characteristics. The long memory characteristics of the extreme series is obviously stronger than that of the original full sample return series itself, which shows that there is a certain dependence between the extreme fluctuation behavior of the market, and the extreme fluctuation behavior of the market is measurable to a certain extent. In addition, the correlation between the maximum series and its corresponding volatility series, between the minimum series and its corresponding volatility series, and between the maximum series and the minimum series are further analyzed. The results show that the different extreme series show their own unique and different intensity interdependence.
[1]Mantegna R N, Stanley H E. Scaling behavior in the dynamics of an economic index[J].Nature,1995,376:46-49. [2]Cont R. Empirical properties of asset returns: Stylized facts and statistical issues[J]. Quantitative Finance, 2001, 1:223-236. [3]Greene M, Fielitz B. Long term dependence in common stock returns[J].Journal of Financial Economics,1977,4(3):339-349. [4]Norouzzadeh P, Jafari G R. Application of multifractal measures to Tehran price index[J]. Physica A, 2005,356: 609-627. [5]Mariani M C, Florescu I, Beccar Varela M P, et al. Long correlations and Levy models applied to the study of memory effects in high frequency (tick) data[J]. Physica A, 2009,388(8):1659-1664. [6]Kasman A, Kasman S, Torun E. Dual long memory property in returns and volatility: Evidence from the CEE countries’ stock markets[J]. Emerging Markets Review, 2009,10(2):122-139. [7]Bisaglia L, Gerolimetto M. Forecasting long memory time series when occasional breaks occur[J]. Economics Letters, 2008,98(3):253-258. [8]Melo Mendes B V, Kolev N. How long memory in volatility affects true dependence structure[J]. International Review of Financial Analysis, 2008, 17(5):1070-1086. [9]Barkoulas J T, Baum C F, Travlos N. Long memory in the greek stock market[J]. Applied Financial Economics,2000, 10(2):177-184. [10] Sensoy A, Tabak B M. Time-varying long term memory in the European union stock markets[J].Physica A,2015,436(1-2):147-158. [11] Caporale G M, Gil-Alana L, Plastun A, et al. Long memory in the Ukrainian stock market and financial crises[J]. Journal of Economics and Finance, 2016, 40(2):235-257. [12] Lonnbark C. Asymmetry with respect to the memory in stock market volatilities[J]. Empirical Economics, 2016, 50(4):1409-1419. [13] Li D, Nishimura Y, Men M. The long memory and the transaction cost in financial markets[J].Physica A, 2016, 442:312-320. [14] Bhar R. Testing for long-term memory in yen/dollar exchange rate[J].Financial Engineering and the Japanese Markets[J].1994,1(2):101-109. [15] Alptekin N. Long memory analysis of USD / TRL exchange rate[J].International Journal of Social Sciences, 2006,1( 2): 111-116. [16] Oh G, Kim S, Eom C. Long-term memory and volatility clustering in high-frequency price changes[J]. Physica A,2008,387( 5/6): 1247-1254. [17] Kang S H, Mclver R, Park S Y et al. Long memory features evolve in the time-varying process in Asia-Pacific foreign exchange markets[J].Procedia Economics and Finance, 2014,14:286-294. [18] Souzaa S R. Long memory testing for Fed Funds futures' contracts[J]. Chaos, Solitons and Fractals, 2008,37(1):180-186. [19] Coakley J. Long memory and structural breaks in commodity future markets[J]. Journal of Futures Markets,2011,31(11):1076-1113. [20] Chkili W, Aloui C, Ngyen D K. Instabilities in the relationships and hedging strategies between crude oil and US stock markets: Do long memory and asymmetry matter?[J]Journal of International markets, institutions & Money,2014,33:354-366. [21] 王鹏,魏宇,王鸿.沪深300股指期货的风险测度模型研究[J].数理统计与管理,2014,33,(4):129-136. Wang Pang, Wei Yu, Wang Hong. Backtesting risk models for CSI300 index futures[J]. Journal of applied statistics and management, 2014,33,(4):129-136. [22] 杨科,田凤平.长记忆性、结构突变条件下中国股市波动率的高频预测[J].管理工程学报,2013,27(2):724-733. Yang Ke, Tian Fengping. Volatility projection with high frequency data under long term memory and structural break in Chinese stock markets[J]. Journal of industrial engineering/engineering management, 2013,27(2):724-733. [23] 曹广喜.中国汇市与股市间的时变冲击影响研究[J].管理科学,2013,26(1):89-100. Cao Guangxi. Research on impact of time-varying shocks from foreign exchange market and stock market[J].Journal of management science, 2013,26(1):89-100. [24] 苑莹,庄新田,金秀.中国股市的日内效应、长记忆性及多重分形性:基于价-量交叉相关性视角[J]. 系统管理学报,2016,25(1):28-35. Yuan Ying, Zhuang Xintian, Jin Xiu. Intraday effects,long memory and multifractal characteristics in Chinese stock markets: a perspective from cross correlation between price and trading volume[J].Journal ofsystems & management, 2016,25(1):28-35. [25] 谭政勋,张欠. 中国股票市场的长期记忆性与趋势预测研究[J]. 统计研究,2016,10:57-66. Tan Zhengxun, Zhang Qian. Research on the long-term memory of Chinese stock market and its trend prediction[J]. Statistical Research,2016,10:57-66. [26] 田存志,程富强,付辉.关于金融市场长记忆性研究的若干争论[J].经济学动态, 2016, 6:141-149. Tian Cunzhi, Cheng Fujiang, Fu Hui.Some arguments on the study of long memory in financial market[J]. Economics perspectives, 2016, 6:141-149. [27] Muchnik L, Bunde A, Havlin S. Long term memory in extreme returns of financial time series [J].Physica A, 2009,388:4145-4150. [28] Eichner J F, Kantelhardt J W, Bunde A, et al. Extreme value statistics in records with long-term persistence[J]. Physical Review E,2006, 73(1Pt2):016130. [29] Norouzzadeh P, Rahmani B. A multifractal detrended fluctuation description of Iranian rial-US dollar exchange rate[J]. Physica A, 2006,367: 328-336.
