Jiang, Zhi-Qiang; Canabarro, Askery; Podobnik, Boris; Stanley, H. Eugene; Zhou, Wei-Xing Early warning of large volatilities based on recurrence interval analysis in Chinese stock markets. (English) Zbl 1400.91664 Quant. Finance 16, No. 11, 1713-1724 (2016). Summary: Forecasting extreme volatility is a central issue in financial risk management. We present a large volatility predicting method based on the distribution of recurrence intervals between successive volatilities exceeding a certain threshold \(Q\), which has a one-to-one correspondence with the expected recurrence time \(\tau_Q\). We find that the recurrence intervals with large \(\tau_Q\) are well approximated by the stretched exponential distribution for all stocks. Thus, an analytical formula for determining the hazard probability \(W(\Delta t|t)\) that a volatility above \(Q\) will occur within a short interval \(\Delta t\) if the last volatility exceeding \(Q\) happened \(t\) periods ago can be directly derived from the stretched exponential distribution, which is found to be in good agreement with the empirical hazard probability from real stock data. Using these results, we adopt a decision-making algorithm for triggering the alarm of the occurrence of the next volatility above \(Q\) based on the hazard probability. Using the ’receiver operator characteristic’ analysis, we find that this prediction method efficiently forecasts the occurrence of large volatility events in real stock data. Our analysis may help us better understand reoccurring large volatilities and quantify more accurately financial risks in stock markets. Cited in 1 Document MSC: 91G70 Statistical methods; risk measures Keywords:extreme volatility; risk estimation; recurrence interval; large volatility forecasting; distribution; hazard probability Software:plfit PDFBibTeX XMLCite \textit{Z.-Q. Jiang} et al., Quant. Finance 16, No. 11, 1713--1724 (2016; Zbl 1400.91664) Full Text: DOI arXiv References: [1] Altmann, E.G. and Kantz, H., Recurrence time analysis, long-term correlations, and extreme events. Phys. Rev. E, 2005, 71, 056106. [2] Bogachev, M.I. and Bunde, A., Memory effects in the statistics of interoccurrence times between large returns in financial record. Phys. Rev. E, 2008, 78, 036114. [3] Bogachev, M.I. and Bunde, A., Improved risk estimation in multifractal records: Application to the value at risk in finance. Phys. Rev. E, 2009a, 80, 026131. [4] Bogachev, M.I. and Bunde, A., On the occurrence and predictability of overloads in telecommunication networks. EPL (Europhys. Lett.), 2009b, 86, 66002. [5] Bogachev, M.I. and Bunde, A., On the predictability of extreme events in records with linear and nonlinear long-range memory: Efficiency and noise robustness. Physica A, 2011, 390, 2240-2250. [6] Bogachev, M.I. and Bunde, A., Universality in the precipitation and river runoff. EPL (Europhys. Lett.), 2012, 97, 48011. [7] Bogachev, M.I., Eichner, J.F. and Bunde, A., Effect of nonlinear correlations on the statistics of return intervals in multifractal data sets. Phys. Rev. Lett., 2007, 99, 240601. [8] Bogachev, M.I., Eichner, J.F. and Bunde, A., On the occurence of extreme events in long-term correlated and multifractal data sets. Pure Appl. Geophys., 2008a, 165, 1195-1207. · Zbl 1191.86020 [9] Bogachev, M.I., Eichner, J.F. and Bunde, A., The effects of multifractality on the statistics of return intervals. Eur. Phys. J. Spec. Top., 2008b, 161, 181-193. [10] Bogachev, M.I., Kireenkov, I.S., Nifontov, E.M. and Bunde, A., Statistics of return intervals between long heartbeat intervals and their usability for online prediction of disorders. New J. Phys., 2009, 11, 063036. [11] Bollen, B. and Inder, B., Estimating daily volatility in financial markets utilizing intraday data. J. Emp. Finance, 2002, 9, 551-562. [12] Bunde, A., Eichner, J.F., Havlin, S. and Kantelhardt, J.W., Return intervals of rare events in records with long-term persistence. Physica A, 2004, 342, 308-314. [13] Bunde, A., Eichner, J.F., Kantelhardt, J.W. and Havlin, S., Long-term memory: A natural mechanism for the clustering of extreme events and anomalous residual times in climate records. Phys. Rev. Lett., 2005, 94, 048701. [14] Cai, S.M., Fu, Z.Q., Zhou, T., Gu, J. and Zhou P.L., Scaling and memory in recurrence intervals of internet traffic. EPL (Europhys. Lett.), 2009, 87, 68001. [15] Chicheportiche, R. and Chakraborti, A., A model-free characterization of recurrences in stationary time series. 2013. arXiv:1302.3704. Available online at: http://arxiv.org/abs/1302.3704 [16] Chicheportiche, R. and Chakraborti, A., Copulas and time series with long-ranged dependencies. Phys. Rev. E, 2014, 89, 042117. [17] Clauset, A., Shalizi, C.R. and Newman, M.E.J., Power-law distributions in empirical data. SIAM Rev., 2009, 51, 661-703. · Zbl 1176.62001 [18] Corral, A., Local distributions and rate fluctuations in a unified scaling law for earthquakes. Phys. Rev. E, 2003, 68, 035102. [19] Dai, Y.H., Xie, W.J., Jiang, Z.Q., Jiang, G.J., and Zhou, W.X., Correlation structure and principal components in global crude oil market. Emp. Econ.Forthcoming. [20] Eichner, J.F., Kantelhardt, J.W., Bunde, A. and Havlin, S., Statistics of return intervals in long-term correlated records. Phys. Rev. E, 2007, 75, 011128. [21] Greco, A., Sorriso-Valvo, L., Carbone, V. and Cidone, S., Waiting time distributions of the volatility in the Italian MIB30 index: Clustering or Poisson functions?Physica A, 2008, 387, 4272-4284. [22] Guo, H.F., Wang, T.N., Li, Y.J. and Fung, H.G., Challenges to China’s new stock market for small and medium-size enterprises: Trading price falls below the IPO price. Technol. Econ. Dev. Econ., 2013, 19, S409-S424. [23] Hallerberg, S., Altmann, E.G., Holstein, D. and Kantz, H., Precursors of extreme increments. Phys. Rev. E, 2007, 75, 016706. [24] Hallerberg, S. and Kantz, H., Influence of the event magnitude on the predictability of an extreme event. Phys. Rev. E, 2008, 77, 011108. [25] He, L.Y. and Chen, S.P., A new approach to quantify power-law cross-correlation and its application to crude oil markets. Physica A, 2011, 390, 3806-3814. [26] Hussein, M.N. and Zhou, Z.G., The initial return and its conditional return volatility: Evidence from the Chinese IPO Market. Rev. Pac. Basin Financ. Mark. Policy, 2014, 17, 1450022. [27] Jeon, W., Moon, H.T., Oh, G., Yang, J.S. and Jung, W.S., Return intervals analysis of the Korean stock market. J. Korean Phys. Soc., 2010, 56, 922-925. [28] Jiang, Z.Q., Chen, W. and Zhou, W.X., Scaling in the distribution of intertrade durations of Chinese stocks. Physica A, 2008, 387, 5818-5825. [29] Jiang, Z.Q., Xie, W.J., Li, M.X., Podobnik, B., Zhou, W.X. and Stanley, H.E., Calling patterns in human communication dynamics. Proc. Natl. Acad. Sci. USA, 2013, 110, 1600-1605. [30] Jiang, Z.Q., Xie, W.J. and Zhou, W.X., Testing the weak-form efficiency of the WTI crude oil futures market. Physica A, 2014, 405, 235-244. [31] Jiang, Z.Q., Zhou, W.X., Sornette, D., Woodard, R., Bastiaensen, K. and Cauwels, P., Bubble diagnosis and prediction of the 2005-2007 and 2008-2009 Chinese stock market bubbles. J. Econ. Behav. Org., 2010, 74, 149-162. [32] Jung, W.S., Wang, F.Z., Havlin, S., Kaizoji, T., Moon, H.T. and Stanley, H.E., Volatility return intervals analysis of the Japanese market. Eur. Phys. J. B, 2008, 62, 113-119. · Zbl 1189.91162 [33] Kaizoji, T. and Kaizoji, M., Power law for the calm-time interval of price changes. Physica A, 2004, 336, 563-570. · Zbl 1068.91033 [34] Lee, J.W., Lee, K.E. and Rikvold, P.A., Waiting-time distribution for Korean stock-market index KOSPI. J. Korean Phys. Soc., 2006, 48, S123-S126. [35] Li, W., Wang, F.Z., Havlin, S. and Stanley, H.E., Financial factor influence on scaling and memory of trading volume in stock market. Phys. Rev. E, 2011, 84, 046112. [36] Liu, C., Jiang, Z.Q., Ren, F. and Zhou, W.X., Scaling and memory in the return intervals of energy dissipation rate in three-dimensional fully developed turbulence. Phys. Rev. E, 2009, 80, 046304. [37] Ludescher, J. and Bunde, A., Universal behavior of the interoccurrence times between losses in financial markets: Independence of the time resolution. Phys. Rev. E, 2014, 90, 062809. [38] Ludescher, J., Tsallis, C. and Bunde, A., Universal behaviour of interoccurrence times between losses in financial markets: An analytical description. EPL (Europhys. Lett.), 2011, 95, 68002. [39] Meng, H., Ren, F., Gu, G.F., Xiong, X., Zhang, Y.J., Zhou, W.X., and Zhang, W, Effects of long memory in the order submission process on the properties of recurrence intervals of large price fluctuations. EPL (Europhys. Lett.), 2012, 98, 38003. [40] Meng, H., Xie, W.J., Jiang, Z.Q., Podobnik, B., Zhou, W.X. and Stanley, H.E., Systemic risk and spatiotemporal dynamics of the US housing market. Sci. Rep., 2014, 4, 3566. [41] Olla, P., Return times for stochastic processes with power-law scaling. Phys. Rev. E, 2007, 76, 011122. [42] Pennetta, C., Distribution of return intervals of extreme events. Eur. Phys. J. B, 2006, 50, 95-98. [43] Podobnik, B., Horvatic, D., Petersen, A.M. and Stanley, H.E., Cross-correlations between volume change and price change. Proc. Natl. Acad. Sci. USA, 2009, 106, 22079-22084. · Zbl 1203.91208 [44] Politi, M. and Scalas, E., Fitting the empirical distribution of intertrade durations. Physica A, 2008, 387, 2025-2034. [45] Qiu, T., Guo, L. and Chen, G., Scaling and memory effect in volatility return interval of the Chinese stock market. Physica A, 2008, 387, 6812-6818. [46] Ren, F., Gu, G.F. and Zhou, W.X., Scaling and memory in the return intervals of realized volatility. Physica A, 2009a, 388, 4787-4796. [47] Ren, F., Guo, L. and Zhou, W.X., Statistical properties of volatility return intervals of Chinese stocks. Physica A2009b, 388, 881-890. [48] Ren, F. and Zhou, W.X., Multiscaling behavior in the volatility return intervals of Chinese indices. EPL (Europhys. Lett.), 2008, 84, 68001. [49] Ren, F. and Zhou, W.X., Recurrence interval analysis of high-frequency financial returns and its application to risk estimation. New J. Phys., 2010a, 12, 075030. [50] Ren, F. and Zhou, W.X., Recurrence interval analysis of trading volumes. Phys. Rev. E, 2010b, 81, 066107. [51] Saichev, A. and Sornette, D., “Universal” distribution of interearthquake times explained. Phys. Rev. Lett., 2006, 97, 078501. [52] Santhanam, M.S. and Kantz, H., Return interval distribution of extreme events and long-term memory. Phys. Rev. E, 2008, 78, 051113. [53] Scalas, E., Gorenflo, R., Luckock, H., Mainardi, F., Mantelli, M. and Raberto, M., Anomalous waiting times in high-frequency financial data. Quant. Finance, 2004, 4, 695-702. [54] Song, D.M., Tumminello, M., Zhou, W.X. and Mantegna, R.N., Evolution of worldwide stock markets, correlation structure, and correlation based graphs. Phys. Rev. E, 2011, 84, 026108. [55] Sornette, D. and Knopoff, L., The paradox of the expected time until the next earthquake. Bull. Seism. Soc. Am., 1997, 87, 789-798. [56] Suo, Y.Y., Wang, D.H. and Li, S.P., Risk estimation of CSI 300 index spot and futures in China from a new perspective. Econ. Model., 2015, 49, 344-353. [57] Wang, F. and Wang, J., Statistical analysis and forecasting of return interval for SSE and model by lattice percolation system and neural network. Comput. Ind. Eng., 2012, 62, 198-205. [58] Wang, F.Z., Weber, P., Yamasaki, K., Havlin, S. and Stanley, H.E., Statistical regularities in the return intervals of volatility. Eur. Phys. J. B, 2007, 55, 123-133. · Zbl 1189.91134 [59] Wang, F.Z., Yamasaki, K., Havlin, S. and Stanley, H.E., Scaling and memory of intraday volatility return intervals in stock markets. Phys. Rev. E, 2006, 73, 026117. [60] Wang, F.Z., Yamasaki, K., Havlin, S. and Stanley, H.E., Indication of multiscaling in the volatility return intervals of stock markets. Phys. Rev. E, 2008, 77, 016109. [61] Wang, F.Z., Yamasaki, K., Havlin, S. and Stanley, H.E., Multifactor analysis of multiscaling in volatility return intervals. Phys. Rev. E, 2009, 79, 016103. [62] Xie, W.J., Jiang, Z.Q. and Zhou, W.X., Extreme value statistics and recurrence intervals of NYMEX energy futures volatility. Econ. Model., 2014, 36, 8-17. [63] Yamasaki, K., Muchnik, L., Havlin, S., Bunde, A. and Stanley, H.E., Scaling and memory in volatility return intervals in financial markets. Proc. Natl. Acad. Sci. USA, 2005, 102, 9424-9428. [64] Yamasaki, K., Muchnik, L., Havlin, S., Bunde, A. and Stanley, H.E., Scaling and memory in return loss intervals: Application to risk estimation, in Proceedings of the Practical Fruits of Econophysics, edited by H. Takayasu, pp. 43-51, 2006 (Springer-Verlag: Berlin). This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.