IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v521y2019icp173-196.html
   My bibliography  Save this article

Modeling non-stationarities in high-frequency financial time series

Author

Listed:
  • Ponta, Linda
  • Trinh, Mailan
  • Raberto, Marco
  • Scalas, Enrico
  • Cincotti, Silvano

Abstract

We study tick-by-tick financial returns for the FTSE MIB index of the Italian Stock Exchange (Borsa Italiana). We confirm previously detected non-stationarities. Scaling properties reported before for other high-frequency financial data are only approximately valid. As a consequence of our empirical analyses, we propose a simple model for non-stationary returns, based on a non-homogeneous normal compound Poisson process. It turns out that our model can approximately reproduce several stylized facts of high-frequency financial time series. Moreover, using Monte Carlo simulations, we analyze order selection for this class of models using three information criteria: Akaike’s information criterion (AIC), the Bayesian information criterion (BIC) and the Hannan–Quinn information criterion (HQ). For comparison, we perform a similar Monte Carlo experiment for the ACD (autoregressive conditional duration) model. Our results show that the information criteria work best for small parameter numbers for the compound Poisson type models, whereas for the ACD model the model selection procedure does not work well in certain cases.

Suggested Citation

  • Ponta, Linda & Trinh, Mailan & Raberto, Marco & Scalas, Enrico & Cincotti, Silvano, 2019. "Modeling non-stationarities in high-frequency financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 173-196.
  • Handle: RePEc:eee:phsmap:v:521:y:2019:i:c:p:173-196
    DOI: 10.1016/j.physa.2019.01.069
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437119300676
    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

    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. Robert F. Engle & Jeffrey R. Russell, 1994. "Forecasting Transaction Rates: The Autoregressive Conditional Duration Model," NBER Working Papers 4966, National Bureau of Economic Research, Inc.
    2. repec:eee:phsmap:v:492:y:2018:i:c:p:814-823 is not listed on IDEAS
    3. Sabrina Camargo & Silvio M. Duarte Queiros & Celia Anteneodo, 2013. "Bridging stylized facts in finance and data non-stationarities," Papers 1302.3197, arXiv.org, revised May 2013.
    4. Lo, Andrew W. & MacKinlay, A. Craig & Zhang, June, 2002. "Econometric models of limit-order executions," Journal of Financial Economics, Elsevier, vol. 65(1), pages 31-71, July.
    5. Enrico Scalas & Rudolf Gorenflo & Hugh Luckock & Francesco Mainardi & Maurizio Mantelli & Marco Raberto, 2004. "Anomalous waiting times in high-frequency financial data," Quantitative Finance, Taylor & Francis Journals, vol. 4(6), pages 695-702.
    6. repec:hin:complx:9072948 is not listed on IDEAS
    7. Luc Bauwens & Pierre Giot, 2000. "The Logarithmic ACD Model: An Application to the Bid-Ask Quote Process of Three NYSE Stocks," Annals of Economics and Statistics, GENES, issue 60, pages 117-149.
    8. Scalas, Enrico, 2006. "The application of continuous-time random walks in finance and economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 362(2), pages 225-239.
    9. Madhavan, Ananth, 2000. "Market microstructure: A survey," Journal of Financial Markets, Elsevier, vol. 3(3), pages 205-258, August.
    10. A. Zaccaria & M. Cristelli & V. Alfi & F. Ciulla & L. Pietronero, 2009. "Asymmetric statistics of order books: The role of discreteness and evidence for strategic order placement," Papers 0906.1387, arXiv.org, revised May 2010.
    11. Bertram, William K, 2004. "An empirical investigation of Australian Stock Exchange data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 341(C), pages 533-546.
    12. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
    13. V. Filimonov & D. Sornette, 2015. "Apparent criticality and calibration issues in the Hawkes self-excited point process model: application to high-frequency financial data," Quantitative Finance, Taylor & Francis Journals, vol. 15(8), pages 1293-1314, August.
    14. Plamen Ch. Ivanov & Ainslie Yuen & Boris Podobnik & Youngki Lee, 2004. "Common Scaling Patterns in Intertrade Times of U. S. Stocks," Papers cond-mat/0403662, arXiv.org.
    15. Parameswaran Gopikrishnan & Vasiliki Plerou & Xavier Gabaix & H. Eugene Stanley, 2000. "Statistical Properties of Share Volume Traded in Financial Markets," Papers cond-mat/0008113, arXiv.org.
    16. M. Goldstein & S. Morris & G. Yen, 2004. "Problems with fitting to the power-law distribution," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 41(2), pages 255-258, September.
    17. Raberto, Marco & Cincotti, Silvano & Focardi, Sergio M. & Marchesi, Michele, 2001. "Agent-based simulation of a financial market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 319-327.
    18. Toke, Ioane Muni & Pomponio, Fabrizio, 2012. "Modelling trades-through in a limit order book using hawkes processes," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy (IfW), vol. 6, pages 1-23.
    19. Engle, Robert F. & Russell, Jeffrey R., 1997. "Forecasting the frequency of changes in quoted foreign exchange prices with the autoregressive conditional duration model," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 187-212, June.
    20. P. Weber & B. Rosenow, 2005. "Order book approach to price impact," Quantitative Finance, Taylor & Francis Journals, vol. 5(4), pages 357-364.
    21. Mainardi, Francesco & Raberto, Marco & Gorenflo, Rudolf & Scalas, Enrico, 2000. "Fractional calculus and continuous-time finance II: the waiting-time distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 468-481.
    22. Z. Eisler & J. Kertész, 2006. "Size matters: some stylized facts of the stock market revisited," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 51(1), pages 145-154, May.
    23. A. Svorenčík & F. Slanina, 2007. "Interacting gaps model, dynamics of order book, and stock-market fluctuations," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 57(4), pages 453-462, June.
    24. Cincotti, Silvano & M. Focardi, Sergio & Marchesi, Michele & Raberto, Marco, 2003. "Who wins? Study of long-run trader survival in an artificial stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 227-233.
    25. Raberto, Marco & Scalas, Enrico & Mainardi, Francesco, 2002. "Waiting-times and returns in high-frequency financial data: an empirical study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 314(1), pages 749-755.
    26. J. Perello & J. Masoliver & A. Kasprzak & R. Kutner, 2008. "A model for interevent times with long tails and multifractality in human communications: An application to financial trading," Papers 0805.1353, arXiv.org, revised Jul 2008.
    27. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters,in: THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78 World Scientific Publishing Co. Pte. Ltd..
    28. Bonanno, Giovanni & Lillo, Fabrizio & Mantegna, Rosario N, 2000. "Dynamics of the number of trades of financial securities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 280(1), pages 136-141.
    29. Youssefmir, Michael & Huberman, Bernardo A., 1997. "Clustered volatility in multiagent dynamics," Journal of Economic Behavior & Organization, Elsevier, vol. 32(1), pages 101-118, January.
    30. Manas, Arnaud, 2012. "The Laplace illusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(15), pages 3963-3970.
    31. Miles Kumaresan & Nataša Krejić, 2010. "A model for optimal execution of atomic orders," Computational Optimization and Applications, Springer, vol. 46(2), pages 369-389, June.
    32. repec:adr:anecst:y:2000:i:60:p:05 is not listed on IDEAS
    33. Scalas, Enrico & Gorenflo, Rudolf & Mainardi, Francesco, 2000. "Fractional calculus and continuous-time finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 376-384.
    34. Chordia, Tarun & Roll, Richard & Subrahmanyam, Avanidhar, 2002. "Order imbalance, liquidity, and market returns," Journal of Financial Economics, Elsevier, vol. 65(1), pages 111-130, July.
    35. V. Gontis & B. Kaulakys, 2006. "Long-range memory model of trading activity and volatility," Papers physics/0606115, arXiv.org.
    36. Hugh Luckock, 2003. "A steady-state model of the continuous double auction," Quantitative Finance, Taylor & Francis Journals, vol. 3(5), pages 385-404.
    37. Gontis, V. & Kaulakys, B. & Ruseckas, J., 2008. "Trading activity as driven Poisson process: Comparison with empirical data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3891-3896.
    38. Giacomo Livan & Jun-ichi Inoue & Enrico Scalas, 2012. "On the non-stationarity of financial time series: impact on optimal portfolio selection," Papers 1205.0877, arXiv.org, revised Jul 2012.
    39. Gençay, Ramazan & Dacorogna, Michel & Muller, Ulrich A. & Pictet, Olivier & Olsen, Richard, 2001. "An Introduction to High-Frequency Finance," Elsevier Monographs, Elsevier, edition 1, number 9780122796715.
    40. Bertram, William K., 2005. "A threshold model for Australian Stock Exchange equities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 346(3), pages 561-576.
    41. Gontis, V. & Ruseckas, J. & Kononovičius, A., 2010. "A long-range memory stochastic model of the return in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(1), pages 100-106.
    42. repec:adr:anecst:y:2000:i:60 is not listed on IDEAS
    43. Esteban Moro & Javier Vicente & Luis G. Moyano & Austin Gerig & J. Doyne Farmer & Gabriella Vaglica & Fabrizio Lillo & Rosario N. Mantegna, 2009. "Market impact and trading profile of large trading orders in stock markets," Papers 0908.0202, arXiv.org.
    44. Constantino Tsallis, 2016. "Inter-occurrence times and universal laws in finance, earthquakes and genomes," Papers 1601.03688, arXiv.org.
    45. Marcus Lim & Richard Coggins, 2005. "The immediate price impact of trades on the Australian Stock Exchange," Quantitative Finance, Taylor & Francis Journals, vol. 5(4), pages 365-377.
    46. Stauffer, Dietrich & Sornette, Didier, 1999. "Self-organized percolation model for stock market fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 271(3), pages 496-506.
    47. Matthieu Wyart & Jean-Philippe Bouchaud & Julien Kockelkoren & Marc Potters & Michele Vettorazzo, 2008. "Relation between bid-ask spread, impact and volatility in order-driven markets," Quantitative Finance, Taylor & Francis Journals, vol. 8(1), pages 41-57.
    48. Hauser, Shmuel & Lauterbach, Beni, 2003. "The Impact of Minimum Trading Units on Stock Value and Price Volatility," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 38(03), pages 575-589, September.
    49. A. Kasprzak & R. Kutner & J. Perelló & J. Masoliver, 2010. "Higher-order phase transitions on financial markets," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 76(4), pages 513-527, August.
    50. Hardle, Wolfgang & Kirman, Alan, 1995. "Nonclassical demand : A model-free examination of price-quantity relations in the Marseille fish market," Journal of Econometrics, Elsevier, vol. 67(1), pages 227-257, May.
    51. Stoll, Hans R & Whaley, Robert E, 1990. "Stock Market Structure and Volatility," Review of Financial Studies, Society for Financial Studies, vol. 3(1), pages 37-71.
    52. repec:spr:eurphb:v:90:y:2017:i:3:d:10.1140_epjb_e2016-70578-3 is not listed on IDEAS
    53. Ioane Muni Toke & Fabrizio Pomponio, 2012. "Modelling Trades-Through in a Limit Order Book Using Hawkes Processes," Post-Print hal-00745554, HAL.
    54. Gontis, V. & Kaulakys, B., 2007. "Modeling long-range memory trading activity by stochastic differential equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 114-120.
    55. Politi, Mauro & Scalas, Enrico, 2008. "Fitting the empirical distribution of intertrade durations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(8), pages 2025-2034.
    56. Cont, Rama & Bouchaud, Jean-Philipe, 2000. "Herd Behavior And Aggregate Fluctuations In Financial Markets," Macroeconomic Dynamics, Cambridge University Press, vol. 4(02), pages 170-196, June.
    57. Gubiec, T. & Wiliński, M., 2015. "Intra-day variability of the stock market activity versus stationarity of the financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 432(C), pages 216-221.
    58. Blume, Marshall E & MacKinley, A Craig & Terker, Bruce, 1989. " Order Imbalances and Stock Price Movements on October 19 and 20, 1987," Journal of Finance, American Finance Association, vol. 44(4), pages 827-848, September.
    59. Zoltan Eisler & Janos Kertesz, 2005. "Size matters: some stylized facts of the stock market revisited," Papers physics/0508156, arXiv.org, revised May 2006.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Cheoljun Eom & Taisei Kaizoji & Enrico Scalas, 2019. "Fat Tails in Financial Return Distributions Revisited: Evidence from the Korean Stock Market," Papers 1904.02567, arXiv.org.

    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:521:y:2019:i:c:p:173-196. See general information about how to correct material in RePEc.

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

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.