IDEAS home Printed from https://ideas.repec.org/a/oup/jfinec/v15y2017i1p139-171..html
   My bibliography  Save this article

Specification Testing in Hawkes Models

Author

Listed:
  • Francine Gresnigt
  • Erik Kole
  • Philip Hans Franses

Abstract

We propose various specification tests for Hawkes models based on the Lagrange Multiplier (LM) principle. Hawkes models can be used to model the occurrence of extreme events in financial markets. Our specific testing focus is on extending a univariate model to a multivariate model, that is, we examine whether there is a conditional dependence between extreme events in markets. Simulations show that the test has good size and power, in particular for sample sizes that are typically encountered in practice. Applying the specification test for dependence to U.S. stocks, bonds, and exchange rate data, we find strong evidence for cross-excitation within segments as well as between segments, which cannot simply be explained by volatility spillovers. Therefore, we recommend that univariate Hawkes models be extended to account for the cross-triggering phenomenon.

Suggested Citation

  • Francine Gresnigt & Erik Kole & Philip Hans Franses, 2017. "Specification Testing in Hawkes Models," Journal of Financial Econometrics, Oxford University Press, vol. 15(1), pages 139-171.
    • Handle: RePEc:oup:jfinec:v:15:y:2017:i:1:p:139-171.
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1093/jjfinec/nbw011
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

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

    for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. van Oordt, Maarten R.C. & Zhou, Chen, 2012. "The simple econometrics of tail dependence," Economics Letters, Elsevier, vol. 116(3), pages 371-373.
    2. P. Hartmann & S. Straetmans & C. G. de Vries, 2004. "Asset Market Linkages in Crisis Periods," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 313-326, February.
    3. Engle, Robert F., 1982. "A general approach to lagrange multiplier model diagnostics," Journal of Econometrics, Elsevier, vol. 20(1), pages 83-104, October.
    4. Baker, Malcolm & Stein, Jeremy C., 2004. "Market liquidity as a sentiment indicator," Journal of Financial Markets, Elsevier, vol. 7(3), pages 271-299, June.
    5. Yosihiko Ogata, 1998. "Space-Time Point-Process Models for Earthquake Occurrences," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(2), pages 379-402, June.
    6. Bowsher, Clive G., 2007. "Modelling security market events in continuous time: Intensity based, multivariate point process models," Journal of Econometrics, Elsevier, vol. 141(2), pages 876-912, December.
    7. Beine, Michel & Cosma, Antonio & Vermeulen, Robert, 2010. "The dark side of global integration: Increasing tail dependence," Journal of Banking & Finance, Elsevier, vol. 34(1), pages 184-192, January.
    8. Gouriéroux, C. & Monfort, A. & Renne, J.P., 2014. "Pricing default events: Surprise, exogeneity and contagion," Journal of Econometrics, Elsevier, vol. 182(2), pages 397-411.
    9. Donald W. K. Andrews, 2003. "Tests for Parameter Instability and Structural Change with Unknown Change Point: A Corrigendum," Econometrica, Econometric Society, vol. 71(1), pages 395-397, January.
    10. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
    11. Hamilton, James D., 1996. "Specification testing in Markov-switching time-series models," Journal of Econometrics, Elsevier, vol. 70(1), pages 127-157, January.
    12. Koutmos, Gregory & Booth, G Geoffrey, 1995. "Asymmetric volatility transmission in international stock markets," Journal of International Money and Finance, Elsevier, vol. 14(6), pages 747-762, December.
    13. Gresnigt, Francine & Kole, Erik & Franses, Philip Hans, 2015. "Interpreting financial market crashes as earthquakes: A new Early Warning System for medium term crashes," Journal of Banking & Finance, Elsevier, vol. 56(C), pages 123-139.
    14. Rogers, Alan J., 1986. "Modified lagrange multiplier tests for problems with one-sided alternatives," Journal of Econometrics, Elsevier, vol. 31(3), pages 341-361, April.
    15. John Y. Campbell & Samuel B. Thompson, 2008. "Predicting Excess Stock Returns Out of Sample: Can Anything Beat the Historical Average?," The Review of Financial Studies, Society for Financial Studies, vol. 21(4), pages 1509-1531, July.
    16. Andrews, Donald W K, 2001. "Testing When a Parameter Is on the Boundary of the Maintained Hypothesis," Econometrica, Econometric Society, vol. 69(3), pages 683-734, May.
    17. Aït-Sahalia, Yacine & Laeven, Roger J.A. & Pelizzon, Loriana, 2014. "Mutual excitation in Eurozone sovereign CDS," Journal of Econometrics, Elsevier, vol. 183(2), pages 151-167.
    18. San‐Lin Chung & Wei‐Che Tsai & Yaw‐Huei Wang & Pei‐Shih Weng, 2011. "The information content of the S&P 500 index and VIX options on the dynamics of the S&P 500 index," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 31(12), pages 1170-1201, December.
    19. Ser-Huang Poon, 2004. "Extreme Value Dependence in Financial Markets: Diagnostics, Models, and Financial Implications," The Review of Financial Studies, Society for Financial Studies, vol. 17(2), pages 581-610.
    20. V. Chavez-Demoulin & A. C. Davison & A. J. McNeil, 2005. "Estimating value-at-risk: a point process approach," Quantitative Finance, Taylor & Francis Journals, vol. 5(2), pages 227-234.
    21. Emmanuel Bacry & Iacopo Mastromatteo & Jean-Franc{c}ois Muzy, 2015. "Hawkes processes in finance," Papers 1502.04592, arXiv.org, revised May 2015.
    22. T. S. Breusch & A. R. Pagan, 1980. "The Lagrange Multiplier Test and its Applications to Model Specification in Econometrics," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(1), pages 239-253.
    23. Giacomo Bormetti & Lucio Maria Calcagnile & Michele Treccani & Fulvio Corsi & Stefano Marmi & Fabrizio Lillo, 2013. "Modelling systemic price cojumps with Hawkes factor models," Papers 1301.6141, arXiv.org, revised Mar 2013.
    24. Longin, Francois & Solnik, Bruno, 1995. "Is the correlation in international equity returns constant: 1960-1990?," Journal of International Money and Finance, Elsevier, vol. 14(1), pages 3-26, February.
    25. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    26. Chavez-Demoulin, V. & McGill, J.A., 2012. "High-frequency financial data modeling using Hawkes processes," Journal of Banking & Finance, Elsevier, vol. 36(12), pages 3415-3426.
    27. Lando, David & Nielsen, Mads Stenbo, 2010. "Correlation in corporate defaults: Contagion or conditional independence?," Journal of Financial Intermediation, Elsevier, vol. 19(3), pages 355-372, July.
    28. Pesaran, M Hashem & Timmermann, Allan, 1995. "Predictability of Stock Returns: Robustness and Economic Significance," Journal of Finance, American Finance Association, vol. 50(4), pages 1201-1228, September.
    29. Grothe, Oliver & Korniichuk, Volodymyr & Manner, Hans, 2014. "Modeling multivariate extreme events using self-exciting point processes," Journal of Econometrics, Elsevier, vol. 182(2), pages 269-289.
    30. Gonzalo, Jesús & Olmo, José, 2005. "Contagion versus flight to quality in financial markets," UC3M Working papers. Economics we051810, Universidad Carlos III de Madrid. Departamento de Economía.
    31. Clive Bowsher, 2002. "Modelling Security Market Events in Continuous Time: Intensity based, Multivariate Point Process Models," Economics Series Working Papers 2002-W22, University of Oxford, Department of Economics.
    32. Ling Hu, 2006. "Dependence patterns across financial markets: a mixed copula approach," Applied Financial Economics, Taylor & Francis Journals, vol. 16(10), pages 717-729.
    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. Molina-Muñoz, Jesús & Mora-Valencia, Andrés & Perote, Javier, 2020. "Market-crash forecasting based on the dynamics of the alpha-stable distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 557(C).
    2. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    3. Francine Gresnigt & Erik Kole & Philip Hans Franses, 2017. "Exploiting Spillovers to Forecast Crashes," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 36(8), pages 936-955, December.
    4. Marcello Rambaldi & Vladimir Filimonov & Fabrizio Lillo, 2016. "Detection of intensity bursts using Hawkes processes: an application to high frequency financial data," Papers 1610.05383, arXiv.org.

    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. Francine Gresnigt & Erik Kole & Philip Hans Franses, 2017. "Exploiting Spillovers to Forecast Crashes," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 36(8), pages 936-955, December.
    2. Gresnigt, Francine & Kole, Erik & Franses, Philip Hans, 2015. "Interpreting financial market crashes as earthquakes: A new Early Warning System for medium term crashes," Journal of Banking & Finance, Elsevier, vol. 56(C), pages 123-139.
    3. Yang Shen & Bin Zou, 2021. "Mean-Variance Portfolio Selection in Contagious Markets," Papers 2110.09417, arXiv.org.
    4. Marcello Rambaldi & Vladimir Filimonov & Fabrizio Lillo, 2016. "Detection of intensity bursts using Hawkes processes: an application to high frequency financial data," Papers 1610.05383, arXiv.org.
    5. Garcia, Rene, 1998. "Asymptotic Null Distribution of the Likelihood Ratio Test in Markov Switching Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(3), pages 763-788, August.
    6. Geweke, J. & Joel Horowitz & Pesaran, M.H., 2006. "Econometrics: A Bird’s Eye View," Cambridge Working Papers in Economics 0655, Faculty of Economics, University of Cambridge.
    7. Dufour, Jean-Marie & Khalaf, Lynda & Bernard, Jean-Thomas & Genest, Ian, 2004. "Simulation-based finite-sample tests for heteroskedasticity and ARCH effects," Journal of Econometrics, Elsevier, vol. 122(2), pages 317-347, October.
    8. Jan Piplack & Stefan Straetmans, 2010. "Comovements Of Different Asset Classes During Market Stress," Pacific Economic Review, Wiley Blackwell, vol. 15(3), pages 385-400, August.
    9. Ji, Jingru & Wang, Donghua & Xu, Dinghai & Xu, Chi, 2020. "Combining a self-exciting point process with the truncated generalized Pareto distribution: An extreme risk analysis under price limits," Journal of Empirical Finance, Elsevier, vol. 57(C), pages 52-70.
    10. Angelos Dassios & Hongbiao Zhao, 2017. "A Generalized Contagion Process With An Application To Credit Risk," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(01), pages 1-33, February.
    11. Hainaut, Donatien & Goutte, Stephane, 2018. "A switching microstructure model for stock prices," LIDAM Discussion Papers ISBA 2018014, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    12. Fuentes, Fernanda & Herrera, Rodrigo & Clements, Adam, 2018. "Modeling extreme risks in commodities and commodity currencies," Pacific-Basin Finance Journal, Elsevier, vol. 51(C), pages 108-120.
    13. Cerrato, Mario & Crosby, John & Kim, Minjoo & Zhao, Yang, 2015. "US Monetary and Fiscal Policies - Conflict or Cooperation?," 2007 Annual Meeting, July 29-August 1, 2007, Portland, Oregon TN 2015-78, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    14. Meitz, Mika & Saikkonen, Pentti, 2021. "Testing for observation-dependent regime switching in mixture autoregressive models," Journal of Econometrics, Elsevier, vol. 222(1), pages 601-624.
    15. Mario Cerrato & John Crosby & Minjoo Kim & Yang Zhao, 2015. "Modeling Dependence Structure and Forecasting Market Risk with Dynamic Asymmetric Copula," Working Papers 2015_15, Business School - Economics, University of Glasgow.
    16. Philipp Hartmann & Stefan Straetmans & Casper de Vries, 2007. "Banking System Stability. A Cross-Atlantic Perspective," NBER Chapters, in: The Risks of Financial Institutions, pages 133-188, National Bureau of Economic Research, Inc.
    17. Buccioli, Alice & Kokholm, Thomas & Nicolosi, Marco, 2019. "Expected shortfall and portfolio management in contagious markets," Journal of Banking & Finance, Elsevier, vol. 102(C), pages 100-115.
    18. Guidolin, Massimo & Hansen, Erwin & Pedio, Manuela, 2019. "Cross-asset contagion in the financial crisis: A Bayesian time-varying parameter approach," Journal of Financial Markets, Elsevier, vol. 45(C), pages 83-114.
    19. Rachele Foschi & Francesca Lilla & Cecilia Mancini, 2020. "Warnings about future jumps: properties of the exponential Hawkes model," Working Papers 13/2020, University of Verona, Department of Economics.
    20. Hamilton, James D., 1996. "Specification testing in Markov-switching time-series models," Journal of Econometrics, Elsevier, vol. 70(1), pages 127-157, January.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

    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:oup:jfinec:v:15:y:2017:i:1:p:139-171.. 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: Oxford University Press (email available below). General contact details of provider: https://edirc.repec.org/data/sofieea.html .

    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.