Element contents
Series: Elements in Econophysics
Recurrence Interval Analysis of Financial Time Series
Published online by Cambridge University Press: 20 February 2024
Summary
Extreme events are ubiquitous in nature and social society, including natural disasters, accident disasters, crises in public health (such as Ebola and the COVID-19 pandemic), and social security incidents (wars, conflicts, and social unrest). These extreme events will heavily impact financial markets and lead to the appearance of extreme fluctuations in financial time series. Such extreme events lack statistics and are thus hard to predict. Recurrence interval analysis provides a feasible solution for risk assessment and forecasting. This Element aims to provide a systemic description of the techniques and research framework of recurrence interval analysis of financial time series. The authors also provide perspectives on future topics in this direction.
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- Series: Elements in EconophysicsOnline ISBN: 9781009381741Publisher: Cambridge University PressPrint publication: 21 March 2024
References
Alessi, L., & Detken, C. (2011). Quasi real time early warning indicators for costly asset price boom/bust cycles: A role for global liquidity. Eur. J. Polit. Econ., 27, 520–533. https://doi.org/10.1016/j.ejpoleco.2011.01.003.CrossRefGoogle Scholar
Alessio, E., Carbone, A., Castelli, G., & Frappietro, V. (2002). Second-order moving average and scaling of stochastic time series. Eur. Phys. J. B, 27(2), 197–200. https://doi.org/10.1140/epjb/e20020150.CrossRefGoogle Scholar
Altmann, E. G., & Kantz, H. (2005). Recurrence time analysis, long-term correlations, and extreme events. Phys. Rev. E, 71, 056106. https://doi.org/10.1103/PhysRevE.71.056106.CrossRefGoogle ScholarPubMed
Amihud, Y. (2002). Illiquidity and stock returns: Cross-section and time-series effects. J. Financ. Markets, 5, 31–56. https://doi.org/10.1016/S1386-4181(01)00024-6.CrossRefGoogle Scholar
Anderson, T. W., & Darling, D. A. (1952). Asymptotic theory of certain “goodness of fit” criteria based on stochastic processes. Ann. Math. Statist., 23(2), 193–212. https://doi.org/10.1214/aoms/1177729437.CrossRefGoogle Scholar
Arianos, S., & Carbone, A. (2007). Detrending moving average algorithm: A closed-form approximation of the scaling law. Physica A, 382(1), 9–15. https://doi.org/10.1016/j.physa.2007.02.074.CrossRefGoogle Scholar
Audit, B., Bacry, E., Muzy, J.- F., & Arnéodo, A. (2002). Wavelet-based estimators of scaling behavior. IEEE Trans. Info. Theory, 48(11), 2938–2954. https://doi.org/10.1109/TIT.2002.802631.CrossRefGoogle Scholar
Babeckỳ, J., Havránek, T., Matějŭ, J., Rusnák, M., Šmídková, K., & Vašíček, B. (2014). Banking, debt, and currency crises in developed countries: Stylized facts and early warning indicators. J. Financ. Stabil., 15, 1–17. https://doi.org/10.1016/j.jfs.2014.07.001.CrossRefGoogle Scholar
Bacry, E., Delour, J., & Muzy, J.- F. (2001). Multifractal random walk. Phys. Rev. E, 64(2), 026103. https://.org/10.1103/PhysRevE.64.026103.CrossRefGoogle ScholarPubMed
Bagnato, L., De Capitani, L., & Punzo, A. (2017). A diagram to detect serial dependencies: An application to transport time series. Qual. Quant., 51, 581–594. https://doi.org/10.1007/s11135-016-0426-y.CrossRefGoogle Scholar
Bashan, A., Bartsch, R., Kantelhardt, J. W., & Havlin, S. (2008). Comparison of detrending methods for fluctuation analysis. Physica A, 387, 5080–5090. https://doi.org/10.1016/j.physa.2008.04.023.CrossRefGoogle Scholar
Benzi, R., Ciliberto, S., Tripiccione, R., Baudet, C., Massaioli, F., & Succi, S. (1993). Extended self-similarity in turbulent flows. Phys. Rev. E, 48(1), R29–R32. https://doi.org/10.1103/PhysRevE.48.R29.CrossRefGoogle ScholarPubMed
Betz, F., Oprică, S., Peltonen, T. A., & Sarlin, P. (2014). Predicting distress in European banks. J. Bank. Financ., 45, 225–241. https://doi.org/10.1016/j.jbankfin.2013.11.041.CrossRefGoogle Scholar
Blender, R., Fraedrich, K., & Sienz, F. (2008). Extreme event return times in long-term memory processes near 1/f. Nonlin. Process Geophys., 15(4), 557–565. https://doi.org/10.5194/npg-15-557-2008.CrossRefGoogle Scholar
Bogachev, M. I., & Bunde, A. (2008). Memory effects in the statistics of interoccurrence times between large returns in financial records. Phys. Rev. E, 78(3), 036114. https://doi.org/10.1103/PhysRevE.78.036114.CrossRefGoogle ScholarPubMed
Bogachev, M. I., & Bunde, A. (2009a). Improved risk estimation in multifractal records: Application to the value at risk in finance. Phys. Rev. E, 80(2), 026131. https://doi.org/10.1103/PhysRevE.80.026131.CrossRefGoogle Scholar
Bogachev, M. I., & Bunde, A. (2009b). On the occurrence and predictability of overloads in telecommunication networks. EPL (Europhys. Lett.), 86, 66002. https://doi.org/10.1209/0295-5075/86/66002.CrossRefGoogle Scholar
Bogachev, M. I., & Bunde, A. (2011). On the predictability of extreme events in records with linear and nonlinear long-range memory: Efficiency and noise robustness. Physica A, 390, 2240–2250. https://doi.org/10.1016/j.physa.2011.02.024.CrossRefGoogle Scholar
Bogachev, M. I., Eichner, J. F., & Bunde, A. (2007). Effect of nonlinear correlations on the statistics of return intervals in multifractal data sets. Phys. Rev. Lett., 99(24), 240601. https://doi.org/10.1103/PhysRevLett.99.240601.CrossRefGoogle ScholarPubMed
Bogachev, M. I., Eichner, J. F., & Bunde, A. (2008a). The effects of multifractality on the statistics of return intervals. Eur. Phys. J. - Spec. Top., 161, 181–193. https://doi.org/10.1140/epjst/e2008-00760-5.CrossRefGoogle Scholar
Bogachev, M. I., Eichner, J. F., & Bunde, A. (2008b). On the occurrence of extreme events in long-term correlated and multifractal data sets. Pure Appl. Geophys., 165, 1195–1207. https://doi.org/10.1007/s00024-008-0353-5.CrossRefGoogle Scholar
Bollen, B., & Inder, B. (2002). Estimating daily volatility in financial markets utilizing intraday data. J. Empir. Financ., 9(5), 551–562. https://doi.org/10.1016/S0927-5398(02)00010-5.CrossRefGoogle Scholar
Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. J. Econometr., 31(3), 307–327. https://doi.org/10.1016/0304-4076(86)90063-1.CrossRefGoogle Scholar
Bunde, A., Bogachev, M. I., & Lennartz, S. (2012). Precipitation and river flow: Long-term memory and predictability of extreme events. In Sharma, A. S., Bunde, A., Dimri, V. P., & Baker, D. N. (eds.), Extreme Events and Natural Hazards: The Complexity Perspective (pp. 139–152). Berlin: AGU Geophysical Monograph Series. https://doi.org/10.1029/2011GM001112CrossRefGoogle Scholar
Bunde, A., Eichner, J. F., Havlin, S., & Kantelhardt, J. W. (2003). The effect of long-term correlations on the return periods of rare events. Physica A, 330, 1–7. https://.org/10.1016/j.physa.2003.08.004.CrossRefGoogle Scholar
Bunde, A., Eichner, J. F., Havlin, S., & Kantelhardt, J. W. (2004). Return intervals of rare events in records with long-term persistence. Physica A, 342, 308–314. https://doi.org/10.1016/j.physa.2004.01.069CrossRefGoogle Scholar
Bunde, A., Eichner, J. F., Kantelhardt, J. W., & Havlin, S. (2005). Long-term memory: A natural mechanism for the clustering of extreme events and anomalous residual times in climate records. Phys. Rev. Lett., 94, 048701. https://doi.org/10.1103/PhysRevLett.94.048701.CrossRefGoogle ScholarPubMed
Bunde, A., & Lennartz, S. (2012). Long-term correlations in earth sciences. Acta Geophys., 60(3), 562–588. https://doi.org/10.2478/s11600-012-0034-8.CrossRefGoogle Scholar
Carbone, A. (2009). Detrending moving average algorithm: A brief review. 2009 IEEE Toronto International Conference Science and Technology for Humanity (TIC-STH), 691–696. https://doi.org/10.1109/TICSTH.2009.5444412.Google Scholar
Carbone, A., & Castelli, G. (2003). Scaling properties of long-range correlated noisy signals: Appplication to financial markets. Proc. SPIE, 5114, 406–414. https://doi.org/10.1117/12.497039.CrossRefGoogle Scholar
Carbone, A., Castelli, G., & Stanley, H. E. (2004a). Analysis of clusters formed by the moving average of a long-range correlated time series. Phys. Rev. E, 69(2), 026105. https://doi.org/10.1103/PhysRevE.69.026105.CrossRefGoogle ScholarPubMed
Carbone, A., Castelli, G., & Stanley, H. E. (2004b). Time-dependent Hurst exponent in financial time series. Physica A, 344(1–2), 267–271. https://doi.org/10.1016/j.physa.2004.06.130.CrossRefGoogle Scholar
Castro, e Silva, A., & Moreira, J. G. (1997). Roughness exponents to calculate multi-affine fractal exponents. Physica A, 235(3), 327–333. https://doi.org/10.1016/S0378-4371(96)00357-3.CrossRefGoogle Scholar
Chen, Z., Ivanov, P. C., Hu, K., & Stanley, H. E. (2002). Effect of nonstationarities on detrended fluctuation analysis. Phys. Rev. E, 65(4), 041107. https://doi.org/10.1103/PhysRevE.65.041107.CrossRefGoogle ScholarPubMed
Chicheportiche, R., & Chakraborti, A. (2014). Copulas and time series with long-ranged dependencies. Phys. Rev. E, 89(4), 042117. https://doi.org/10.1103/PhysRevE.89.042117.CrossRefGoogle ScholarPubMed
Chicheportiche, R., & Chakraborti, A. (2017). A model-free characterization of recurrences in stationary time series. Physica A, 474, 312–318. https://doi.org/10.1016/j.physa.2017.01.073.CrossRefGoogle Scholar
Christensen, I., & Li, F.- C. (2014). Predicting financial stress events: A signal extraction approach. J. Financ. Stabil., 14, 54–65. https://doi.org/10.1016/j.jfs.2014.08.005.CrossRefGoogle Scholar
Clauset, A., Shalizi, C. R., & Newman, M. E. J. (2009). Power-law distributions in empirical data. SIAM Rev., 51(4), 661–703. https://doi.org/10.1137/070710111.CrossRefGoogle Scholar
Dai, Y.- H., Jiang, Z.- Q., & Zhou, W.- X. (2018). Forecasting extreme atmospheric events with a recurrence-interval-analysis-based autoregressive conditional duration model. Sci. Rep., 8, 16264. https://doi.org/10.1038/s41598-018-34584-4.CrossRefGoogle ScholarPubMed
Deng, W., & Wang, J. (2015). Statistical analysis on multifractal detrended cross-correlation coefficient for return interval by oriented percolation. Int. J. Mod. Phys. C, 26(1), 1550002. https://doi.org/10.1142/S0129183115500023.CrossRefGoogle Scholar
Dong, Y. F., & Wang, J. (2013). Fluctuation behavior of financial return interval series model for percolation on Sierpinski carpet lattice. Fractals, 21(3–4), 1350023. https://doi.org/10.1142/S0218348X13500230.CrossRefGoogle Scholar
Drożdż, S., Kwapień, J., Oświȩcimka, P., & Rak, R. (2009). Quantitative features of multifractal subtleties in time series. EPL (Europhys. Lett.), 88(6), 60003. https://doi.org/10.1209/0295-5075/88/60003.CrossRefGoogle Scholar
Duca, M. L., & Peltonen, T. A. (2013). Assessing systemic risks and predicting systemic events. J. Bank. Financ., 37(7), 2183–2195. https://doi.org/10.1016/j.jbankfin.2012.06.010.CrossRefGoogle Scholar
Eichner, J. F., Kantelhardt, J. W., Bunde, A., & Havlin, S. (2007). Statistics of return intervals in long-term correlated records. Phys. Rev. E, 75(1), 011128. https://doi.org/10.1103/PhysRevE.75.011128.CrossRefGoogle ScholarPubMed
Eisler, Z., & Kertész, J. (2006). Size matters: Some stylized facts of the stock market revisited. Eur. Phys. J. B, 51(1), 145–154. https://doi.org/10.1140/epjb/e2006-00189-6.CrossRefGoogle Scholar
El-Shagi, M., Knedlik, T., & von Schweinitz, G. (2013). Predicting financial crises: The (statistical) significance of the signals approach. J. Int. Money Financ., 35, 76–103. https://doi.org/10.1016/j.jimonfin.2013.02.001.CrossRefGoogle Scholar
Engle, R. F., & Russell, J. R. (1998). Autoregressive conditional duration: A new model for irregularly spaced transaction data. Econometrica, 66(5), 1127–1162. https://doi.org/10.2307/2999632.CrossRefGoogle Scholar
Fawcett, T. (2006). An introduction to roc analysis. Pattern Recognit. Lett., 27(8), 861–874. https://doi.org/10.1016/j.patrec.2005.10.010.CrossRefGoogle Scholar
Filimonov, V., Wheatley, S., & Sornette, D. (2015). Effective measure of endogeneity for the autoregressive conditional duration point processes via mapping to the self-excited Hawkes process. Commun. Nonlinear Sci. Numer. Simul., 22(1–3), 23–37. https://doi.org/10.1016/j.cnsns.2014.08.042.CrossRefGoogle Scholar
Gao, X.- L., Shao, Y.- H., Yang, Y.- H., & Zhou, W.- X. (2022). Do the global grain spot markets exhibit multifractal nature? Chaos Solitons Fractals, 164, 112663. https://doi.org/10.1016/j.chaos.2022.112663.CrossRefGoogle Scholar
Garman, M. B., & Klass, M. J. (1980). On the estimation of security price volatilities from historical data. J. Business, 53, 67–78. https://www.jstor.org/stable/2352358CrossRefGoogle Scholar
Gontis, V. (2016). Interplay between endogenous and exogenous fluctuations in financial markets. Acta Phys. Pol. A, 129(5), 1023–1031. https://doi.org/10.12693/APhysPolA.129.1023.CrossRefGoogle Scholar
Gontis, V., Havlin, S., Kononovicius, A., Podobnik, B., & Stanley, H. E. (2016). Stochastic model of financial markets reproducing scaling and memory in volatility return intervals. Physica A, 462, 1091–1102. https://doi.org/10.1016/j.physa.2016.06.143.CrossRefGoogle Scholar
González, M. C., Hidalgo, C. A., & Barabási, A.- L. (2008). Understanding individual human mobility patterns. Nature, 453, 779–782. https://doi.org/10.1038/nature06958.CrossRefGoogle ScholarPubMed
Gopikrishnan, P., Meyer, M., Amaral, L. A. N., & Stanley, H. E. (1998). Inverse cubic law for the distribution of stock price variations. Eur. Phys. J. B, 3(2), 139–140. https://doi.org/10.1007/s100510050292.CrossRefGoogle Scholar
Gresnigt, F., Kole, E., & Franses, P. H. (2015). Interpreting financial market crashes as earthquakes: A new early warning system for medium term crashes. J. Bank. Financ., 56, 123–139. https://doi.org/10.1016/j.jbankfin.2015.03.003.CrossRefGoogle Scholar
Gu, G.- F., Chen, W., & Zhou, W.- X. (2008). Empirical distributions of Chinese stock returns at different microscopic timescales. Physica A, 387(2–3), 495–502. https://doi.org/10.1016/j.physa.2007.10.012.CrossRefGoogle Scholar
Gu, G.- F., & Zhou, W.- X. (2009). Emergence of long memory in stock volatility from a modified Mike-Farmer model. EPL (Europhys.Lett.), 86(4), 48002. https://doi.org/10.1209/0295-5075/86/48002.CrossRefGoogle Scholar
Gu, G.- F., & Zhou, W.- X. (2010). Detrending moving average algorithm for multifractals. Phys. Rev. E, 82(1), 011136. https://doi.org/10.1103/PhysRevE.82.011136.CrossRefGoogle ScholarPubMed
Harris, L. (1986). A transaction data study of weekly and intradaily patterns in stock returns. J. Financ. Econ., 16(1), 99–117. https://doi.org/10.1016/0304-405X(86)90044-9.CrossRefGoogle Scholar
Hautsch, N. (2003). Assessing the risk of liquidity suppliers on the basis of excess demand intensities. J. Financ. Econometr., 1(2), 189–215. https://doi.org/10.1093/jjfinec/nbg010.CrossRefGoogle Scholar
He, L.- Y., & Chen, S.- P. (2011). A new approach to quantify power-law cross-correlation and its application to crude oil markets. Physica A, 390(21), 3806–3814. https://doi.org/10.1016/j.physa.2011.06.013.CrossRefGoogle Scholar
Helmstetter, A., & Sornette, D. (2002a). Diffusion of epicenters of earthquake aftershocks, Omori’s law, and generalized continuous-time random walk models. Phys. Rev. E, 66(6), 061104. https://doi.org/10.1103/PhysRevE.66.061104.CrossRefGoogle ScholarPubMed
Helmstetter, A., & Sornette, D. (2002b). Subcritical and supercritical regimes in epidemic models of earthquake aftershocks. J. Geophys. Res., 107(B10), 2237. https://doi.org/10.1029/2001JB001580Google Scholar
Heneghan, C., & McDarby, G. (2000). Establishing the relation between detrended fluctuation analysis and power spectral density analysis for stochastic processes. Phys. Rev. E, 62, 6103–6110. https://doi.org/10.1103/PhysRevE.62.6103CrossRefGoogle ScholarPubMed
Hill, B. M. (1975). A simple general approach to inference about the tail of a distribution. Ann. Statist., 3, 1163–1174. https://doi.org/10.1214/aos/1176343247CrossRefGoogle Scholar
Hong, B. H., Lee, K. E., & Lee, J. W. (2007). Power law of quiet time distribution in the Korean stock-market. Physica A, 377(2), 576–582. https://doi.org/10.1016/j.physa.2006.11.076.CrossRefGoogle Scholar
Hu, K., Ivanov, P. C., Chen, Z., Carpena, P., & Stanley, H. E. (2001). Effect of trends on detrended fluctuation analysis. Phys. Rev. E, 64(1), 011114. https://doi.org/10.1103/PhysRevE.64.011114.CrossRefGoogle ScholarPubMed
Hurst, H. E. (1951). Long-term storage capacity of reservoirs. Trans. Amer. Soc. Civil Eng., 116, 770–808. https://doi.org/10.1061/TACEAT.0006518CrossRefGoogle Scholar
Jeon, W., Moon, H.- T., Oh, G., Yang, J.- S., & Jung, W.- S. (2010). Return intervals analysis of the Korean stock market. J. Korean Phys. Soc., 56(3), 922–925. https://doi.org/10.3938/jkps.56.922.Google Scholar
Ji, L.-J., Zhou, W.-X., Liu, H.-F. et al. (2009). R/S method for unevenly sampled time series: Application to detecting long-term temporal dependence of droplets transiting through a fixed spatial point in gas-liquid two-phase turbulent jets. Physica A, 388(17), 3345–3354. https://doi.org/10.1016/j.physa.2009.05.006.CrossRefGoogle Scholar
Jiang, Z.- Q., Canabarro, A., Podobnik, B., Stanley, H. E., & Zhou, W.- X. (2016). Early warning of large volatilities based on recurrence interval analysis in Chinese stock markets. Quant. Financ., 16(11), 1713–1724. https://doi.org/10.1080/14697688.2016.1175656.CrossRefGoogle Scholar
Jiang, Z.-Q., Wang, G.-J., Canabarro, A. et al. (2018). Short term prediction of extreme returns based on the recurrence interval analysis. Quant. Financ., 18(3), 353–370. https://doi.org/10.1080/14697688.2017.1373843.CrossRefGoogle Scholar
Jiang, Z.- Q., Xie, W.- J., & Zhou, W.- X. (2014). Testing the weak-form efficiency of the WTI crude oil futures market. Physica A, 405, 235–244. https://doi.org/10.1016/j.physa.2014.02.042.CrossRefGoogle Scholar
Jiang, Z.- Q., Xie, W.- J., Zhou, W.- X., & Sornette, D. (2019). Multifractal analysis of financial markets: A review. Rep. Prog. Phys., 82(12), 125901. https://doi.org/10.1088/1361-6633/ab42fb.CrossRefGoogle ScholarPubMed
Jung, W.-S., Wang, F.-Z., Havlin, S. et al. (2008). Volatility return intervals analysis of the Japanese market. Eur. Phys. J. B, 62, 113–119. https://doi.org/10.1140/epjb/e2008-00123-0.CrossRefGoogle Scholar
Kaizoji, T., & Kaizoji, M. (2004). Power law for the calm-time interval of price changes. Physica A, 336(3–4), 563–570. https://doi.org/10.1016/j.physa.2003.12.054.CrossRefGoogle Scholar
Kantelhardt, J. W., Koscielny-Bunde, E., Rego, H. H. A., Havlin, S., & Bunde, A. (2001). Detecting long-range correlations with detrended fluctuation analysis. Physica A, 295(3–4), 441–454. https://doi.org/10.1016/S0378-4371(01)00144-3.CrossRefGoogle Scholar
Kantelhardt, J. W., Zschiegner, S. A., Koscielny-Bunde, E. et al. (2002). Multifractal detrended fluctuation analysis of nonstationary time series. Physica A, 316(1–4), 87–114. https://doi.org/10.1016/S0378-4371(02)01383-3.CrossRefGoogle Scholar
Kitt, R., & Kalda, J. (2005). Properties of low-variability periods in financial time series. Physica A, 345(3–4), 622–634. https://doi.org/10.1016/j.physa.2004.07.015.CrossRefGoogle Scholar
Kolmogorov, A. N. (1933). Sulla determinazione empirica di una legge di distribuzione. Giorn. Ist. Ital. Attuar., 4(1), 83–91. (Translated in English as “On the empirical determination of a distribution law” in Shiryayev, A. N. (ed.), Selected Works of A. N. Kolmogorov, 139–146, Springer, 1992) https://doi.org/10.1007/978-94-011-2260-3_15.Google Scholar
Laherrère, J., & Sornette, D. (1998). Stretched exponential distributions in nature and economy: “Fat tails” with characteristic scales. Eur. Phys. J. B, 2(4), 525–539. https://doi.org/10.1007/s100510050276.CrossRefGoogle Scholar
Lee, J., Lee, K., & Rikvold, P. (2006). Waiting-time distribution for Korean stock-market index KOSPI. J. Korean Phys. Soc., 48, S123–S126. https://www.jkps.or.kr/journal/view.html?uid=7698&vmd=FullGoogle Scholar
Lennartz, S., Livina, V., Bunde, A., & Havlin, S. (2008). Long-term memory in earthquakes and the distribution of interoccurrence times. EPL (Europhys. Lett.), 81, 69001. https://doi.org/10.1209/0295-5075/81/69001.CrossRefGoogle Scholar
Li, W., Wang, F., Havlin, S., & Stanley, H. E. (2011). Financial factor influence on scaling and memory of trading volume in stock market. Phys. Rev. E, 84(4), 046112. https://doi.org/10.1103/PhysRevE.84.046112.CrossRefGoogle ScholarPubMed
Li, W.- S., & Liaw, S.- S. (2015). Return volatility interval analysis of stock indexes during a financial crash. Physica A, 434, 151-163. https://doi.org/10.1016/j.physa.2015.03.063.CrossRefGoogle Scholar
Li, W.- Z., Zhai, J.- R., Jiang, Z.- Q., Wang, G.- J., & Zhou, W.- X. (2022). Predicting tail events in a RIA-EVT-copula framework. Physica A, 600, 127524. https://doi.org/10.1016/j.physa.2022.127524.CrossRefGoogle Scholar
Liu, C., Jiang, Z.- Q., Ren, F., & Zhou, W.- X. (2009). Scaling and memory in the return intervals of energy dissipation rate in three-dimensional fully developed turbulence. Phys. Rev. E, 80(4), 046304. https://doi.org/10.1103/PhysRevE.80.046304.CrossRefGoogle ScholarPubMed
Livina, V. N., Havlin, S., & Bunde, A. (2005). Memory in the occurrence of earthquakes. Phys. Rev. Lett., 95, 208501. https://doi.org/10.1103/PhysRevLett.95.208501.CrossRefGoogle ScholarPubMed
Livina, V. N., Tuzov, S., Havlin, S., & Bunde, A. (2005). Recurrence intervals between earthquakes strongly depend on history. Physica A, 348, 591–595. https://doi.org/10.1016/j.physa.2004.08.032.CrossRefGoogle Scholar
Ljung, G. M., & Box, G. E. P. (1978). On a measure of lack of fit in time series models. Biometrika, 65(2), 297–303. https://doi.org/10.1093/biomet/65.2.297.CrossRefGoogle Scholar
Lo, A. W. (1991). Long-term memory in stock market prices. Econometrica, 59, 1279–1313. https://doi.org/10.2307/2938368CrossRefGoogle Scholar
Lo, A. W., & Wang, J. (2000). Trading volume: Definitions, data analysis, and implications of portfolio theory. Rev. Financ. Stud., 13(2), 257–300. https://doi.org/10.1093/rfs/13.2.257.CrossRefGoogle Scholar
Luc, B., & Pierre, G. (2000). The logarithmic ACD model: An application to the bid-ask quote process of three NYSE stocks. Annales d’Économie et de Statistique, 60(60), 117–149. https://doi.org/10.2307/20076257.Google Scholar
Ludescher, J., & Bunde, A. (2014). Universal behavior of the interoccurrence times between losses in financial markets: Independence of the time resolution. Phys. Rev. E, 90(6), 062809. https://doi.org/10.1103/PhysRevE.90.062809.CrossRefGoogle ScholarPubMed
Ludescher, J., Tsallis, C., & Bunde, A. (2011). Universal behaviour of interoccurrence times between losses in financial markets: An analytical description. EPL (Europhys.Lett.), 95(6), 68002. https://doi.org/10.1209/0295-5075/95/68002.CrossRefGoogle Scholar
Lunde, A. (1999). A Generalized Gamma Autoregressive Conditional Duration Model. (Working paper)Google Scholar
Malevergne, Y., Pisarenko, V., & Sornette, D. (2005). Empirical distributions of stock returns: Between the stretched exponential and the power law? Quant. Financ., 5(4), 379–401. https://doi.org/10.1080/14697680500151343.CrossRefGoogle Scholar
Malevergne, Y., & Sornette, D. (2006). Extreme Financial Risks: From Dependence to Risk Management. Berlin: Springer.Google Scholar
Mandelbrot, B. B., & Wallis, J. R. (1969a). Computer experiments with fractional Gaussian noise. Part 2, rescaled ranges and spectra. Water Resour. Res., 5, 242–259. https://doi.org/10.1029/WR005i001p00228CrossRefGoogle Scholar
Mandelbrot, B. B., & Wallis, J. R. (1969b). Robustness of the rescaled range R/S in the measurement of noncyclic long run statistical dependence. Water Resour. Res., 5, 967–988. https://doi.org/10.1029/WR005i005p00967CrossRefGoogle Scholar
Matsushita, R., Gleria, I., Figueiredo, A., & Silva, S. D. (2007). Are pound and euro the same currency? Phys. Lett. A, 368(3–4), 173–180. https://doi.org/10.1016/j.physleta.2007.03.085.CrossRefGoogle Scholar
Meng, H., Ren, F., Gu, G.-F. et al. (2012). Effects of long memory in the order submission process on the properties of recurrence intervals of large price fluctuations. EPL (Europhys.Lett.), 98(3), 38003. https://doi.org/10.1209/0295-5075/98/38003.CrossRefGoogle Scholar
Mike, S., & Farmer, J. D. (2008). An empirical behavioral model of liquidity and volatility. J. Econ. Dyn. Control, 32(1), 200–234. https://doi.org/10.1016/j.jedc.2007.01.025.CrossRefGoogle Scholar
Moloney, N. R., & Davidsen, J. (2009). Extreme value statistics and return intervals in long-range correlated uniform deviates. Phys. Rev. E, 79, 041131. https://doi.org/10.1103/PhysRevE.79.041131.CrossRefGoogle ScholarPubMed
Montanari, A., Taqqu, M. S., & Teverovsky, V. (1999). Estimating long-range dependence in the presence of periodicity: An empirical study. Math. Comput. Model., 29(10–12), 217–228. https://doi.org/10.1016/S0895-7177(99)00104-1.CrossRefGoogle Scholar
Mu, G.- H., & Zhou, W.- X. (2010). Tests of nonuniversality of the stock return distributions in an emerging market. Phys. Rev. E, 82(6), 066103. https://doi.org/10.1103/PhysRevE.82.066103.CrossRefGoogle Scholar
Newey, W. K., & West, K. D. (1987). A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica, 55(3), 703–708. https://doi.org/10.2307/1913610.CrossRefGoogle Scholar
Ng, K., Peiris, S., & Gerlach, R. (2014). Estimation and forecasting with logarithmic autoregressive conditional duration models: A comparative study with an application. Expert Sys. Appl., 41(7), 3323–3332. https://doi.org/10.1016/j.eswa.2013.11.024.CrossRefGoogle Scholar
Olla, P. (2007). Return times for stochastic processes with power-law scaling. Phys. Rev. E, 76, 011122. https://doi.org/10.1103/PhysRevE.76.011122CrossRefGoogle ScholarPubMed
Openshaw, S., & Connolly, C. J. (1977). Empirically derived deterrence functions for maximum performance spatial interaction models. Environ. Planning A, 9(9), 1068–1079. https://doi.org/10.1068/a091067.CrossRefGoogle Scholar
Oświȩcimka, P., Drożdż, S., Kwapień, J., & Górski, A. Z. (2013). Effect of detrending on multifractal characteristics. Acta Phys. Pol. A, 123(3), 597–603. https://doi.org/10.12693/APhysPolA.123.597.CrossRefGoogle Scholar
Ouyang, F. Y., Zheng, B., & Jiang, X. F. (2014). Spatial and temporal structures of four financial markets in greater China. Physica A, 402, 236–244. https://doi.org/10.1016/j.physa.2014.02.006.CrossRefGoogle Scholar
Pearson, E. S., & Stephens, M. A. (1962). The goodness-of-fit tests on
and
. Biometrika, 49, 397–402. https://doi.org/10.1093/biomet/49.3-4.397Google Scholar
Pei, A. Q., & Wang, J. (2015). Graphic analysis and multifractal on percolation-based return interval series. Int. J. Mod. Phys. C, 26(12), 1550137. https://doi.org/10.1142/S0129183115501375.CrossRefGoogle Scholar
Peng, C.- K., Buldyrev, S. V., Havlin, S., Simons, M., Stanley, H. E., & Goldberger, A. L. (1994). Mosaic organization of DNA nucleotides. Phys. Rev. E, 49(2), 1685–1689. https://doi.org/10.1103/PhysRevE.49.1685.CrossRefGoogle ScholarPubMed
Podobnik, B., Horvatic, D., Petersen, A. M., & Stanley, H. E. (2009). Cross-correlations between volume change and price change. Proc. Natl. Acad. Sci. U. S. A., 106(52), 22079–22084. https://doi.org/10.1073/pnas.0911983106.CrossRefGoogle ScholarPubMed
Press, W., Teukolsky, S., Vetterling, W., & Flannery, B. (1996). Numerical Recipes in FORTRAN: The Art of Scientific Computing. Cambridge: Cambridge University Press.Google Scholar
Press, W., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. (2007). Numerical Recipes: The Art of Scientific Computing (3rd ed.). Cambridge: Cambridge University Press.Google Scholar
Qiu, T., Guo, L., & Chen, G. (2008). Scaling and memory effect in volatility return interval of the Chinese stock market. Physica A, 387, 6812–6818. https://doi.org/10.1016/j.physa.2008.09.002.CrossRefGoogle Scholar
Reboredo, J. C., Rivera-Castro, M. A., & de Assis, E. M. (2014). Power-law behaviour in time durations between extreme returns. Quant. Financ., 14(12), 2171–2183. https://doi.org/10.1080/14697688.2013.822538.CrossRefGoogle Scholar
Ren, F., Gu, G.- F., & Zhou, W.- X. (2009). Scaling and memory in the return intervals of realized volatility. Physica A, 388(22), 4787–4796. https://doi.org/10.1016/j.physa.2009.08.009.CrossRefGoogle Scholar
Ren, F., Guo, L., & Zhou, W.- X. (2009). Statistical properties of volatility return intervals of Chinese stocks. Physica A, 388(6), 881–890. https://doi.org/10.1016/j.physa.2008.12.005.CrossRefGoogle Scholar
Ren, F., & Zhou, W.- X. (2008). Multiscaling behavior in the volatility return intervals of Chinese indices. EPL (Europhys.Lett.), 84(6), 68001. https://doi.org/10.1209/0295-5075/84/68001.CrossRefGoogle Scholar
Ren, F., & Zhou, W.- X. (2010). Recurrence interval analysis of high-frequency financial returns and its application to risk estimation. New J. Phys., 12, 075030. https://doi.org/10.1088/1367-2630/12/7/075030.CrossRefGoogle Scholar
Saichev, A., & Sornette, D. (2006). “Universal” distribution of interearthquake times explained. Phys. Rev. Lett., 97(7), 078501. https://doi.org/10.1103/PhysRevLett.97.078501.CrossRefGoogle ScholarPubMed
Saichev, A., & Sornette, D. (2007). Theory of earthquake recurrence times. J. Geophys. Res.-Solid Earth, 112(B4), B04313. https://doi.org/10.1029/2006JB004536.CrossRefGoogle Scholar
Santhanam, M. S., & Kantz, H. (2008). Return interval distribution of extreme events and long-term memory. Phys. Rev. E, 78(5), 051113. https://doi.org/10.1103/PhysRevE.78.051113.CrossRefGoogle ScholarPubMed
Sarlin, P. (2013). On policymakers’ loss functions and the evaluation of early warning systems. Econ. Lett., 119(1), 1–7. https://doi.org/10.1016/j.econlet.2012.12.030.CrossRefGoogle Scholar
Schumann, A. Y., & Kantelhardt, J. W. (2011). Multifractal moving average analysis and test of multifractal model with tuned correlations. Physica A, 390(14), 2637–2654. https://doi.org/10.1016/j.physa.2011.03.002.CrossRefGoogle Scholar
Serletis, A., & Rosenberg, A. A. (2007). The Hurst exponent in energy futures prices. Physica A, 380, 325–332. https://doi.org/10.1016/j.physa.2007.02.055.CrossRefGoogle Scholar
Serletis, A., & Rosenberg, A. A. (2009). Mean reversion in the US stock market. Chaos Solitons Fractals, 40(4), 2007–2015. https://doi.org/10.1016/j.chaos.2007.09.085.CrossRefGoogle Scholar
Shao, Y.- H., Gu, G.- F., Jiang, Z.- Q., & Zhou, W.- X. (2015). Effects of polynomial trends on detrending moving average analysis. Fractals, 23(3), 1550034. https://doi.org/10.1142/S0218348X15500346.CrossRefGoogle Scholar
Shao, Y.- H., Gu, G.- F., Jiang, Z.- Q., Zhou, W.- X., & Sornette, D. (2012). Comparing the performance of FA, DFA and DMA using different synthetic long-range correlated time series. Sci. Rep., 2, 835. https://doi.org/10.1038/srep00835.CrossRefGoogle ScholarPubMed
Shiller, R. J. (1981). Do stock prices move too much to be justified by subsequent changes in dividends? Am. Econ. Rev., 71(3), 421–436. https://doi.org/10.3386/w0456.Google Scholar
Smirnov, N. V. (1939). On the estimation of the discrepancy between empirical curves of distribution for two independent samples. Bull. Math. Univ. Moscow, 2(2), 3–4.Google Scholar
Sornette, D. (2003a). Critical market crashes. Phys. Rep., 378(1), 1–98. https://doi.org/10.1016/S0370-1573(02)00634-8.CrossRefGoogle Scholar
Sornette, D. (2004). Critical Phenomena in Natural Sciences (2nd ed.). Berlin: Springer.Google Scholar
Sornette, D. (2009). Dragon-kings, black swans and the prediction of crises. Int. J. Terraspace Sci. Eng., 2, 1–18.Google Scholar
Sornette, D., & Knopoff, L. (1997). The paradox of the expected time until the next earthquake. Bull. Seism. Soc. Am., 87, 789–798. https://doi.org/10.1785/BSSA0870040789CrossRefGoogle Scholar
Sornette, D., & Ouillon, G. (2012). Dragon-kings: Mechanisms, statistical methods and empirical evidence. Eur. Phys. J.-Spec. Top., 205(1), 1–26. https://doi.org/10.1140/epjst/e2012-01559-5.CrossRefGoogle Scholar
Stephens, M. A. (1964). The distribution of the goodness-of-fit statistic,
. II. Biometrika, 51, 393–397. https://doi.org/10.1093/biomet/51.3-4.393Google Scholar
Stephens, M. A. (1970). Use of the Kolmogorov-Smirnov, Cramér-Von Mises and related statistics without extensive tables. J. R. Stat. Soc. B, 32(1), 115–122. https://doi.org/10.1111/j.2517-6161.1970.tb00821.xGoogle Scholar
Stephens, M. A. (1974). EDF statistics for goodness of fit and some comparisons. J. Am. Stat. Assoc., 69, 730–737. https://doi.org/10.1080/01621459.1974.10480196CrossRefGoogle Scholar
Suo, Y.- Y., Wang, D.- H., & Li, S.- P. (2015). Risk estimation of CSI 300 index spot and futures in China from a new perspective. Econ. Model., 49, 344–353. https://doi.org/10.1016/j.econmod.2015.05.011.CrossRefGoogle Scholar
Talkner, P., & Weber, R. O. (2000). Power spectrum and detrended fluctuation analysis: Application to daily temperatures. Phys. Rev. E, 62, 150–160. https://doi.org/10.1103/PhysRevE.62.150CrossRefGoogle ScholarPubMed
Taqqu, M. S., Teverovsky, V., & Willinger, W. (1995). Estimators for long-range dependence: An empirical study. Fractals, 3(4), 785–798. https://doi.org/10.1142/S0218348X95000692.CrossRefGoogle Scholar
Teverovsky, V., Taqqu, M. S., & Willinger, W. (1999). A critical look at Lo’s modified R/S statistic. J. Stat. Plann. Inference, 80, 211–227. https://doi.org/10.1016/S0378-3758(98)00250-XCrossRefGoogle Scholar
Vandewalle, N., & Ausloos, M. (1998). Crossing of two mobile averages: A method for measuring the roughness exponent. Phys. Rev. E, 58(5), 6832–6834. https://doi.org/10.1103/PhysRevE.58.6832.CrossRefGoogle Scholar
Varotsos, P. A., Sarlis, N. V., Tanaka, H. K., & Skordas, E. S. (2005). Some properties of the entropy in the natural time. Phys. Rev. E, 71(3), 032102. https://doi.org/10.1103/PhysRevE.71.032102.CrossRefGoogle ScholarPubMed
Vodenska-Chitkushev, I., Wang, F.- Z., Weber, P., Yamasaki, K., Havlin, S., & Stanley, H. E. (2008). Comparison between volatility return intervals of the S&P 500 index and two common models. Eur. Phys. J. B, 61, 217–223. https://doi.org/10.1140/epjb/e2008-00066-4.CrossRefGoogle Scholar
Wang, F., Weber, P., Yamasaki, K., Havlin, S., & Stanley, H. E. (2007). Statistical regularities in the return intervals of volatility. Eur. Phys. J. B, 55, 123–133. https://doi.org/10.1140/epjb/e2006-00356-9.CrossRefGoogle Scholar
Wang, F., Yamasaki, K., Havlin, S., & Stanley, H. (2006). Scaling and memory of intraday volatility return intervals in stock markets. Phys. Rev. E, 73(2), 026117. https://doi.org/10.1103/PhysRevE.73.026117.CrossRefGoogle ScholarPubMed
Wang, F., Yamasaki, K., Havlin, S., & Stanley, H. E. (2008). Indication of multiscaling in the volatility return intervals of stock markets. Phys. Rev. E, 77(1), 016109. https://doi.org/10.1103/PhysRevE.77.016109.CrossRefGoogle ScholarPubMed
Wang, F.- Z., Yamasaki, K., Havlin, S., & Stanley, H. E. (2009). Multifactor analysis of multiscaling in volatility return intervals. Phys. Rev. E, 79, 016103.https://doi.org/10.1103/PhysRevE.79.016103.CrossRefGoogle ScholarPubMed
Weber, P., Wang, F., Vodenska-Chitkushev, I., Havlin, S., & Stanley, H. E. (2007). Relation between volatility correlations in financial markets and Omori processes occurring on all scales. Phys. Rev. E, 76(1), 016109. https://doi.org/10.1103/PhysRevE.76.016109.CrossRefGoogle ScholarPubMed
Weber, R. O., & Talkner, P. (2001). Spectra and correlations of climate data from days to decades. J. Geophys. Res., 106, 20131–20144. https://doi.org/10.1029/2001GL014170.CrossRefGoogle Scholar
Wehrli, A., & Sornette, D. (2022). The excess volatility puzzle explained by financial noise amplification from endogenous feedbacks. Sci. Rep., 12(1), 18895. https://doi.org/10.1038/s41598-022-20879-0.CrossRefGoogle ScholarPubMed
Wood, R. A., McInish, T. H., & Ord, J. K. (1985). An investigation of transactions data for NYSE stocks. J. Financ., 40(3), 723–739. https://doi.org/10.2307/2327796.CrossRefGoogle Scholar
Wu, G.-H., Qiu, L., Stephen, M., et al., (2014). Statistics of extreme events in Chinese stock markets. Chin. Phys. B, 23(12), 128901. https://doi.org/10.1088/1674-1056/23/12/128901.CrossRefGoogle Scholar
Xie, W.- J., Jiang, Z.- Q., & Zhou, W.- X. (2014). Extreme value statistics and recurrence intervals of NYMEX energy futures volatility. Econ. Model., 36, 8–17. https://doi.org/10.1016/j.econmod.2013.09.011.CrossRefGoogle Scholar
Xu, L. M., Ivanov, P. C., Hu, K. et al. (2005). Quantifying signals with power-law correlations: A comparative study of detrended fluctuation analysis and detrended moving average techniques. Phys. Rev. E, 71(21), 051101. https://doi.org/10.1103/PhysRevE.71.051101.CrossRefGoogle ScholarPubMed
Yakovlev, G., Turcotte, D. L., Rundle, J. B., & Rundle, P. B. (2006). Simulation-based distributions of earthquake recurrence times on the San Andreas fault system. Bull. Seismol. Soc. Amer., 96(6), 1995–2007. https://doi.org/10.1785/0120050183.CrossRefGoogle Scholar
Yamasaki, K., Muchnik, L., Havlin, S., Bunde, A., & Stanley, H. E. (2005). Scaling and memory in volatility return intervals in financial markets. Proc. Natl. Acad. Sci. U. S. A., 102(26), 9424–9428. https://doi.org/10.1073/pnas.0502613102.CrossRefGoogle ScholarPubMed
Yamasaki, K., Muchnik, L., Havlin, S., Bunde, A., & Stanley, H. E. (2006). Scaling and memory in return loss intervals: Application to risk estimation. In Takayasu, H. (ed.), Practical Fruits of Econophysics (pp. 43–51). Berlin: Springer-Verlag. https://doi.org/10.1007/4-431-28915-1_7.CrossRefGoogle Scholar
Yang, G., & Wang, J. (2016). Complexity and multifractal of volatility duration for agent-based financial dynamics and real markets. Fractals, 24(4), 1650052. https://doi.org/10.1142/S0218348X16500523.CrossRefGoogle Scholar
Yuan, Y., Zhuang, X.- t., Liu, Z.- y., & Huang, W.- q. (2014). Analysis of the temporal properties of price shock sequences in crude oil markets. Physica A, 394, 235–246. https://doi.org/10.1016/j.physa.2013.09.040.CrossRefGoogle Scholar
Zhang, C., Pu, Z., & Zhou, Q. (2018). Sustainable energy consumption in northeast Asia: A case from China’s fuel oil futures market. Sustainability, 10(1), 261. https://doi.org/10.3390/su10010261.CrossRefGoogle Scholar
Zhang, J.- H., Wang, J., & Shao, J.- G. (2010). Finite-range contact process on the market return intervals distributions. Adv. Complex Sys., 13, 643–657. https://doi.org/10.1142/S0219525910002797.CrossRefGoogle Scholar
Zhao, X., Shang, P., & Lin, A. (2016). Universal and non-universal properties of recurrence intervals of rare events. Physica A, 448, 132–143. https://doi.org/10.1016/j.physa.2015.12.082.CrossRefGoogle Scholar
Zhou, W.- J., Wang, Z.- X., & Guo, H.- M. (2016). Modelling volatility recurrence intervals in the Chinese commodity futures market. Physica A, 457, 514–525. https://doi.org/10.1016/j.physa.2016.03.044.CrossRefGoogle Scholar
Zhou, W.- J., Wu, X.- L., Pan, J., & Wang, Z.- X. (2020). Recurrence intervals analysis of CSI 300 future based on high frequency data. Econ. Comput. Econ. Cybern. Stud., 54(2), 299–314. https://doi.org/10.24818/18423264/54.2.20.18.Google Scholar
Zhou, W.- X. (2009). The components of empirical multifractality in financial returns. EPL (Europhys.Lett.), 88(2), 28004. https://doi.org/10.1209/0295-5075/88/28004.CrossRefGoogle Scholar
Zhou, W.- X. (2012a). Determinants of immediate price impacts at the trade level in an emerging order-driven market. New J. Phys., 14, 023055. https://doi.org/10.1088/1367-2630/14/2/023055.CrossRefGoogle Scholar
Zhou, W.- X. (2012b). Finite-size effect and the components of multifractality in financial volatility. Chaos Solitons Fractals, 45(2), 147–155. https://doi.org/10.1016/j.chaos.2011.11.004.CrossRefGoogle Scholar
Zhou, W.- X. (2012c). Universal price impact functions of individual trades in an order-driven market. Quant. Financ., 12(8), 1253–1263. https://doi.org/10.1080/14697688.2010.504733.CrossRefGoogle Scholar
Zhou, W.- X., Sornette, D., & Yuan, W.- K. (2006). Inverse statistics and multifractality of exit distances in 3D fully developed turbulence. Physica D, 214(1), 55–62. doi: https://doi.org/10.1016/j.physd.2005.12.004.CrossRefGoogle Scholar