IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v490y2018icp1555-1574.html
   My bibliography  Save this article

Networks of volatility spillovers among stock markets

Author

Listed:
  • Baumöhl, Eduard
  • Kočenda, Evžen
  • Lyócsa, Štefan
  • Výrost, Tomáš

Abstract

In our network analysis of 40 developed, emerging and frontier stock markets during the 2006–2014 period, we describe and model volatility spillovers during both the global financial crisis and tranquil periods. The resulting market interconnectedness is depicted by fitting a spatial model incorporating several exogenous characteristics. We document the presence of significant temporal proximity effects between markets and somewhat weaker temporal effects with regard to the US equity market — volatility spillovers decrease when markets are characterized by greater temporal proximity. Volatility spillovers also present a high degree of interconnectedness, which is measured by high spatial autocorrelation. This finding is confirmed by spatial regression models showing that indirect effects are much stronger than direct effects; i.e., market-related changes in ‘neighboring’ markets (within a network) affect volatility spillovers more than changes in the given market alone, suggesting that spatial effects simply cannot be ignored when modeling stock market relationships. Our results also link spillovers of escalating magnitude with increasing market size, market liquidity and economic openness.

Suggested Citation

  • Baumöhl, Eduard & Kočenda, Evžen & Lyócsa, Štefan & Výrost, Tomáš, 2018. "Networks of volatility spillovers among stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 1555-1574.
  • Handle: RePEc:eee:phsmap:v:490:y:2018:i:c:p:1555-1574
    DOI: 10.1016/j.physa.2017.08.123
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437117308543
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

    File URL: https://libkey.io/10.1016/j.physa.2017.08.123?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Baumöhl, Eduard & Kočenda, Evžen & Lyócsa, Štefan & Výrost, Tomáš, 2018. "Networks of volatility spillovers among stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 1555-1574.
    2. Geert Bekaert & Michael Ehrmann & Marcel Fratzscher & Arnaud Mehl, 2014. "The Global Crisis and Equity Market Contagion," Journal of Finance, American Finance Association, vol. 69(6), pages 2597-2649, December.
    3. Lyócsa, Štefan & Výrost, Tomáš & Baumöhl, Eduard, 2012. "Stock market networks: The dynamic conditional correlation approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(16), pages 4147-4158.
    4. da Silva, Marcus Fernandes & de Area Leão Pereira, Éder Johnson & da Silva Filho, Aloisio Machado & de Castro, Arleys Pereira Nunes & Miranda, José Garcia Vivas & Zebende, Gilney Figueira, 2016. "Quantifying the contagion effect of the 2008 financial crisis between the G7 countries (by GDP nominal)," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 453(C), pages 1-8.
    5. Lahmiri, Salim, 2017. "A study on chaos in crude oil markets before and after 2008 international financial crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 389-395.
    6. Pin-te Lin, 2013. "Examining volatility spillover in Asian REIT markets," Applied Financial Economics, Taylor & Francis Journals, vol. 23(22), pages 1701-1705, November.
    7. Franklin Allen & Douglas Gale, 2000. "Financial Contagion," Journal of Political Economy, University of Chicago Press, vol. 108(1), pages 1-33, February.
    8. Kaminsky, Graciela L. & Reinhart, Carmen M., 2000. "On crises, contagion, and confusion," Journal of International Economics, Elsevier, vol. 51(1), pages 145-168, June.
    9. Mensi, Walid & Beljid, Makram & Boubaker, Adel & Managi, Shunsuke, 2013. "Correlations and volatility spillovers across commodity and stock markets: Linking energies, food, and gold," Economic Modelling, Elsevier, vol. 32(C), pages 15-22.
    10. Boubaker, Heni & Raza, Syed Ali, 2016. "On the dynamic dependence and asymmetric co-movement between the US and Central and Eastern European transition markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 459(C), pages 9-23.
    11. Sofiane Aboura & Julien Chevallier, 2014. "Cross‐market spillovers with ‘volatility surprise’," Review of Financial Economics, John Wiley & Sons, vol. 23(4), pages 194-207, November.
    12. Arghyrou, Michael G. & Kontonikas, Alexandros, 2012. "The EMU sovereign-debt crisis: Fundamentals, expectations and contagion," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 22(4), pages 658-677.
    13. Nobi, Ashadun & Maeng, Seong Eun & Ha, Gyeong Gyun & Lee, Jae Woo, 2014. "Effects of global financial crisis on network structure in a local stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 407(C), pages 135-143.
    14. Garcia, René & Tsafack, Georges, 2011. "Dependence structure and extreme comovements in international equity and bond markets," Journal of Banking & Finance, Elsevier, vol. 35(8), pages 1954-1970, August.
    15. Lu, Feng-bin & Hong, Yong-miao & Wang, Shou-yang & Lai, Kin-keung & Liu, John, 2014. "Time-varying Granger causality tests for applications in global crude oil markets," Energy Economics, Elsevier, vol. 42(C), pages 289-298.
    16. Caetano, Marco Antonio Leonel & Yoneyama, Takashi, 2015. "Boolean network representation of contagion dynamics during a financial crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 417(C), pages 1-6.
    17. Lyócsa, Štefan & Výrost, Tomáš & Baumöhl, Eduard, 2019. "Return spillovers around the globe: A network approach," Economic Modelling, Elsevier, vol. 77(C), pages 133-146.
    18. Hui, Eddie Chi-man & Chan, Ka Kwan Kevin, 2014. "The global financial crisis: Is there any contagion between real estate and equity markets?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 216-225.
    19. Bekaert, Geert & Harvey, Campbell R., 1997. "Emerging equity market volatility," Journal of Financial Economics, Elsevier, vol. 43(1), pages 29-77, January.
    20. Jozef Baruník, Evzen Kocenda and Lukáa Vácha, 2015. "Volatility Spillovers Across Petroleum Markets," The Energy Journal, International Association for Energy Economics, vol. 0(Number 3).
    21. Lahmiri, Salim, 2017. "Asymmetric and persistent responses in price volatility of fertilizers through stable and unstable periods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 405-414.
    22. Kuzubaş, Tolga Umut & Ömercikoğlu, Inci & Saltoğlu, Burak, 2014. "Network centrality measures and systemic risk: An application to the Turkish financial crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 203-215.
    23. Yanan Li & David E. Giles, 2015. "Modelling Volatility Spillover Effects Between Developed Stock Markets and Asian Emerging Stock Markets," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 20(2), pages 155-177, March.
    24. Dewandaru, Ginanjar & Masih, Rumi & Masih, A. Mansur M., 2015. "Why is no financial crisis a dress rehearsal for the next? Exploring contagious heterogeneities across major Asian stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 241-259.
    25. Výrost, Tomáš & Lyócsa, Štefan & Baumöhl, Eduard, 2015. "Granger causality stock market networks: Temporal proximity and preferential attachment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 427(C), pages 262-276.
    26. Sandoval, Leonidas & Franca, Italo De Paula, 2012. "Correlation of financial markets in times of crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 187-208.
    27. John Beirne & Guglielmo Maria Caporale & Marianne Schulze-Ghattas & Nicola Spagnolo, 2013. "Volatility Spillovers and Contagion from Mature to Emerging Stock Markets," Review of International Economics, Wiley Blackwell, vol. 21(5), pages 1060-1075, November.
    28. James P. Lesage, 2008. "An Introduction to Spatial Econometrics," Revue d'économie industrielle, De Boeck Université, vol. 0(3), pages 19-44.
    29. Liu, Xueyong & An, Haizhong & Huang, Shupei & Wen, Shaobo, 2017. "The evolution of spillover effects between oil and stock markets across multi-scales using a wavelet-based GARCH–BEKK model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 374-383.
    30. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    31. Beirne, John & Fratzscher, Marcel, 2013. "The pricing of sovereign risk and contagion during the European sovereign debt crisis," Journal of International Money and Finance, Elsevier, vol. 34(C), pages 60-82.
    32. Engle, Robert F & Ng, Victor K, 1993. "Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, vol. 48(5), pages 1749-1778, December.
    33. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    34. Mink, Mark, 2015. "Measuring stock market contagion: Local or common currency returns?," Emerging Markets Review, Elsevier, vol. 22(C), pages 18-24.
    35. Cheung, Yin-Wong & Ng, Lilian K., 1996. "A causality-in-variance test and its application to financial market prices," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 33-48.
    36. Francis X. Diebold & Kamil Yilmaz, 2009. "Measuring Financial Asset Return and Volatility Spillovers, with Application to Global Equity Markets," Economic Journal, Royal Economic Society, vol. 119(534), pages 158-171, January.
    37. Higgins, Matthew L & Bera, Anil K, 1992. "A Class of Nonlinear ARCH Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(1), pages 137-158, February.
    38. Choi, Pilsun & Nam, Kiseok, 2008. "Asymmetric and leptokurtic distribution for heteroscedastic asset returns: The SU-normal distribution," Journal of Empirical Finance, Elsevier, vol. 15(1), pages 41-63, January.
    39. Whitney K. Newey & Kenneth D. West, 1994. "Automatic Lag Selection in Covariance Matrix Estimation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(4), pages 631-653.
    40. Liu, Li & Wang, Yudong, 2014. "Cross-correlations between spot and futures markets of nonferrous metals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 400(C), pages 20-30.
    41. Anagnostidis, P. & Varsakelis, C. & Emmanouilides, C.J., 2016. "Has the 2008 financial crisis affected stock market efficiency? The case of Eurozone," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 116-128.
    42. Lahmiri, Salim, 2015. "Long memory in international financial markets trends and short movements during 2008 financial crisis based on variational mode decomposition and detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 130-138.
    43. Engle, Robert F. & White (the late), Halbert (ed.), 1999. "Cointegration, Causality, and Forecasting: Festschrift in Honour of Clive W. J. Granger," OUP Catalogue, Oxford University Press, number 9780198296836, Decembrie.
    44. Majapa, Mohamed & Gossel, Sean Joss, 2016. "Topology of the South African stock market network across the 2008 financial crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 445(C), pages 35-47.
    45. Luchtenberg, Kimberly F. & Vu, Quang Viet, 2015. "The 2008 financial crisis: Stock market contagion and its determinants," Research in International Business and Finance, Elsevier, vol. 33(C), pages 178-203.
    46. Kenourgios, Dimitris & Padhi, Puja, 2012. "Emerging markets and financial crises: Regional, global or isolated shocks?," Journal of Multinational Financial Management, Elsevier, vol. 22(1), pages 24-38.
    47. Al Rahahleh, Naseem & Bhatti, M. Ishaq, 2017. "Co-movement measure of information transmission on international equity markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 470(C), pages 119-131.
    48. Kanjamapornkul, K. & Pinčák, Richard & Bartoš, Erik, 2016. "The study of Thai stock market across the 2008 financial crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 117-133.
    49. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    50. Wu, Guojun, 2001. "The Determinants of Asymmetric Volatility," Review of Financial Studies, Society for Financial Studies, vol. 14(3), pages 837-859.
    51. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    52. Kim, Jun Sik & Ryu, Doojin, 2014. "Intraday price dynamics in spot and derivatives markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 247-253.
    53. Diebold, Francis X. & Yilmaz, Kamil, 2015. "Financial and Macroeconomic Connectedness: A Network Approach to Measurement and Monitoring," OUP Catalogue, Oxford University Press, number 9780199338306, Decembrie.
    54. Chiang, Thomas C. & Jeon, Bang Nam & Li, Huimin, 2007. "Dynamic correlation analysis of financial contagion: Evidence from Asian markets," Journal of International Money and Finance, Elsevier, vol. 26(7), pages 1206-1228, November.
    55. Nazlioglu, Saban & Erdem, Cumhur & Soytas, Ugur, 2013. "Volatility spillover between oil and agricultural commodity markets," Energy Economics, Elsevier, vol. 36(C), pages 658-665.
    56. Hui, Eddie C.M. & Chen, Jia, 2012. "Investigating the change of causality in emerging property markets during the financial tsunami," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(15), pages 3951-3962.
    57. Hong, Yongmiao, 2001. "A test for volatility spillover with application to exchange rates," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 183-224, July.
    58. Baruník, Jozef & Kočenda, Evžen & Vácha, Lukáš, 2016. "Gold, oil, and stocks: Dynamic correlations," International Review of Economics & Finance, Elsevier, vol. 42(C), pages 186-201.
    59. Sensoy, A. & Yuksel, S. & Erturk, M., 2013. "Analysis of cross-correlations between financial markets after the 2008 crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(20), pages 5027-5045.
    60. Zakoian, Jean-Michel, 1994. "Threshold heteroskedastic models," Journal of Economic Dynamics and Control, Elsevier, vol. 18(5), pages 931-955, September.
    61. Kang, Sang Hoon & Cheong, Chongcheul & Yoon, Seong-Min, 2013. "Intraday volatility spillovers between spot and futures indices: Evidence from the Korean stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(8), pages 1795-1802.
    62. Diebold, Francis X. & Yilmaz, Kamil, 2012. "Better to give than to receive: Predictive directional measurement of volatility spillovers," International Journal of Forecasting, Elsevier, vol. 28(1), pages 57-66.
    63. Hwang, Eugene & Min, Hong-Ghi & Kim, Bong-Han & Kim, Hyeongwoo, 2013. "Determinants of stock market comovements among US and emerging economies during the US financial crisis," Economic Modelling, Elsevier, vol. 35(C), pages 338-348.
    64. Baur, Dirk G., 2012. "Financial contagion and the real economy," Journal of Banking & Finance, Elsevier, vol. 36(10), pages 2680-2692.
    65. Kantar, Ersin & Keskin, Mustafa & Deviren, Bayram, 2012. "Analysis of the effects of the global financial crisis on the Turkish economy, using hierarchical methods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(7), pages 2342-2352.
    66. Kang, Sang Hoon & Cheong, Chongcheul & Yoon, Seong-Min, 2011. "Structural changes and volatility transmission in crude oil markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4317-4324.
    67. Güloğlu, Bülent & Kaya, Pınar & Aydemir, Resul, 2016. "Volatility transmission among Latin American stock markets under structural breaks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 330-340.
    68. Ji, Qiang & Guo, Jian-Feng, 2015. "Market interdependence among commodity prices based on information transmission on the Internet," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 426(C), pages 35-44.
    69. Mobarek, Asma & Muradoglu, Gulnur & Mollah, Sabur & Hou, Ai Jun, 2016. "Determinants of time varying co-movements among international stock markets during crisis and non-crisis periods," Journal of Financial Stability, Elsevier, vol. 24(C), pages 1-11.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lyócsa, Štefan & Výrost, Tomáš & Baumöhl, Eduard, 2019. "Return spillovers around the globe: A network approach," Economic Modelling, Elsevier, vol. 77(C), pages 133-146.
    2. Štefan Lyócsa & Roman Horváth, 2018. "Stock Market Contagion: a New Approach," Open Economies Review, Springer, vol. 29(3), pages 547-577, July.
    3. Výrost, Tomáš & Lyócsa, Štefan & Baumöhl, Eduard, 2015. "Granger causality stock market networks: Temporal proximity and preferential attachment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 427(C), pages 262-276.
    4. Lahmiri, Salim & Uddin, Gazi Salah & Bekiros, Stelios, 2017. "Clustering of short and long-term co-movements in international financial and commodity markets in wavelet domain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 947-955.
    5. Baruník, Jozef & Kočenda, Evžen & Vácha, Lukáš, 2016. "Asymmetric connectedness on the U.S. stock market: Bad and good volatility spillovers," Journal of Financial Markets, Elsevier, vol. 27(C), pages 55-78.
    6. Zhang, Weiping & Zhuang, Xintian, 2019. "The stability of Chinese stock network and its mechanism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 748-761.
    7. Borjigin, Sumuya & Gao, Ting & Sun, Yafei & An, Biao, 2020. "For evil news rides fast, while good news baits later?—A network based analysis in Chinese stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    8. Newaz, Mohammad Khaleq & Park, Jin Suk, 2019. "The impact of trade intensity and Market characteristics on asymmetric volatility, spillovers and asymmetric spillovers: Evidence from the response of international stock markets to US shocks," The Quarterly Review of Economics and Finance, Elsevier, vol. 71(C), pages 79-94.
    9. Lyócsa, Štefan & Baumöhl, Eduard, 2015. "Similarity of emerging market returns under changing market conditions: Markets in the ASEAN-4, Latin America, Middle East, and BRICs," Economic Systems, Elsevier, vol. 39(2), pages 253-268.
    10. Zouheir Mighri, 2018. "On the Dynamic Linkages Among International Emerging Currencies," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 16(2), pages 427-473, June.
    11. Kenourgios, Dimitris & Naifar, Nader & Dimitriou, Dimitrios, 2016. "Islamic financial markets and global crises: Contagion or decoupling?," Economic Modelling, Elsevier, vol. 57(C), pages 36-46.
    12. Baumöhl, Eduard & Lyócsa, Štefan, 2014. "Volatility and dynamic conditional correlations of worldwide emerging and frontier markets," Economic Modelling, Elsevier, vol. 38(C), pages 175-183.
    13. Roman Horváth & Štefan Lyócsa & Eduard Baumöhl, 2018. "Stock market contagion in Central and Eastern Europe: unexpected volatility and extreme co-exceedance," The European Journal of Finance, Taylor & Francis Journals, vol. 24(5), pages 391-412, March.
    14. Yarovaya, Larisa & Brzeszczyński, Janusz & Lau, Chi Keung Marco, 2017. "Asymmetry in spillover effects: Evidence for international stock index futures markets," International Review of Financial Analysis, Elsevier, vol. 53(C), pages 94-111.
    15. Trucíos, Carlos, 2019. "Forecasting Bitcoin risk measures: A robust approach," International Journal of Forecasting, Elsevier, vol. 35(3), pages 836-847.
    16. Antonakakis, Nikolaos & Cunado, Juncal & Filis, George & Gabauer, David & de Gracia, Fernando Perez, 2020. "Oil and asset classes implied volatilities: Investment strategies and hedging effectiveness," Energy Economics, Elsevier, vol. 91(C).
    17. Jeffrey Chu & Stephen Chan & Saralees Nadarajah & Joerg Osterrieder, 2017. "GARCH Modelling of Cryptocurrencies," JRFM, MDPI, vol. 10(4), pages 1-15, October.
    18. Lorenzo Cappiello & Robert F. Engle & Kevin Sheppard, 2006. "Asymmetric Dynamics in the Correlations of Global Equity and Bond Returns," Journal of Financial Econometrics, Oxford University Press, vol. 4(4), pages 537-572.
    19. Baumöhl, Eduard, 2013. "Stock market integration between the CEE-4 and the G7 markets: Asymmetric DCC and smooth transition approach," MPRA Paper 43834, University Library of Munich, Germany.
    20. Luo, Jiawen & Marfatia, Hardik A. & Ji, Qiang & Klein, Tony, 2023. "Co-volatility and asymmetric transmission of risks between the global oil and China's futures markets," Energy Economics, Elsevier, vol. 117(C).

    More about this item

    Keywords

    Volatility spillovers; Stock markets; Shock transmission; Granger causality network; Spatial regression; Financial crisis;
    All these keywords.

    JEL classification:

    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • F01 - International Economics - - General - - - Global Outlook
    • G01 - Financial Economics - - General - - - Financial Crises
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:490:y:2018:i:c:p:1555-1574. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.