Jean-Michel ZAKOIAN

Grade : Professeur des Universités (CMC)

Mail : zakoian[arrowbase]

ResearchBooksJournal articlesTeachingWork in progressOther

Research Interests


Time Series, Theoretical and Financial Econometrics, Statistics.

Previous and current positions

Research Fellow at CREST, Full-time (2007- )
Professor, Applied Mathematics, Université Lille III (2000-... on leave since 2007).
Maître de Conférences, Applied mathematics, Université Lille I (1993-2000).



Ecole Nationale de la Statistique et de l'Administration Economique
5 Avenue Henry Le Chatelier 91120 Palaiseau




Curriculum Vitae

Citations profile



Editorial Activities

Associate Editor for Econometric Theory (2012 - ).                                                                           

Associate Editor for Scandinavian Journal of statistics (2019 - )

Associate Editor for Journal of Time Series Analysis (2013 - )

Guest Associate Editor for Annals of Computational and Financial Econometrics (2011-2015).





Economica, Collection "Economie et statistiques avancées",  2009,
605 pages, with C. Francq.


GARCH  Models -  Structure, Estimation and Finance Applications 
John Wiley,  2010, ISBN 978-0-470-68391-0
with C. Francq.



GARCH  Models -  Structure, Estimation and Finance Applications - 2nd Edition
John Wiley,  2019, ISBN 978-1119313571
with C. Francq.

Journal articles



  1. Adaptiveness of the empirical distribution of residuals in semi-parametric conditional loaction-scale models. Forthcoming in Bernoulli, with C. Francq, 2021. 
  2. Testing the existence of moments for GARCH processes. Forthcoming in Journal of Econometrics, with C. Francq, 2021.
  3. Virtual Historical Simulation for estimating the conditional VaR of large portfoliosJournal of Econometrics, 217, 356-380, with C. Francq, 2020.
  4. Consistent Pseudo-Maximum Likelihood Estimators and Groups of TransformationsEconometrica 87, 327-345, with C.  Gouriéroux and A. Monfort, 2019.
  5. Mixed Causal-Noncausal AR Processes and the Modelling of Explosive Bubbles. Econometric Theory, 35, 1234-1270, with S. Fries, 2019.
  6. Functional GARCH models: the quasi-likelihood approach and its applicationsJournal of Econometrics, 209, 353-375, with C. Cerovecki, S. Hörmann and C. Francq, 2019.
  7. Estimation risk for the VaR of portfolios driven by semi-parametric multivariate modelsJournal of Econometrics, 205, 381-401, with C. Francq, 2018.
  8. Goodness-of-fit tests for log-GARCH and EGARCH modelsTest,   27, 27-51, with O. Wintenberger and C. Francq, 2018.
  9. Local explosion modelling by noncausal process. Journal of the Royal Statistical Society: Series B, 79, 737-756, with C. Gouriéroux, 2017.
  10. Estimating multivariate GARCH models equation by equation. Journal of the Royal Statistical Society: Series B,   2016, 78, 613-635, with C. Francq.
  11. Intrinsic liquidity in conditional volatility Models.  Annals of Economics and Statistics 123-124, 225-246, with S. Darolles, G. Lefol and C. Francq, 2016.
  12. Looking for efficient QML estimation of conditional VaRs at multiple risk levels.    Annals of Economics and Statistics 123-124, 9-28, with  C. Francq, 2016.
  13. Variance targeting estimation of multivariate GARCH models, Journal of Financial Econometrics,  14, 353-382, with C. Francq and L. Horvath, 2016.
  14. Asymptotic inference in multiple-threshold double autoregressive modelsJournal of Econometrics,  189, 415-427, with D. Li and S. Ling, 2015.
  15. On uniqueness of moving average representations of heavy-tailed stationary processes. Journal of Time Series Analysis, 36, 876-887, with C. Gouriéroux, 2015.
  16. Risk-parameter estimation in volatility models. Journal of Econometrics, 184, 158-173 with C. Francq, 2015.
  17. Comment on "Quasi-Maximum Likelihood Estimation of GARCH Models with Heavy Tailed Likelihoods" by J. Fan, L. Qi et D. Xiu. Journal of Business & Economic Statistics, 32, 198-201 with C. Francq, 2014.
  18. Multi-level conditional VaR estimation in dynamic models. In Modeling Dependence in Econometrics. Advances in Intelligent Systems and Computing Volume 251. Edts: V-N. Huynh et al., Springer, with C. Francq, 2014.
  19. Inference in non stationary asymmetric GARCH models. Annals of Statistics, 41:4, 70-98 with C. Francq, 2013.
  20. GARCH models without positivity constraints: Exponential or Log GARCH? Journal of Econometrics, 177, 34-46 with C. Francq and O. Wintenberger, 2013.
  21. Estimating the Marginal Law of a Time Series with Applications to Heavy Tailed Distributions. Journal of Business and Economic Statistics, 31:4, 412-425 with C. Francq, 2013.
  22. Optimal predictions of powers of conditionally heteroskedastic processes. Journal of the Royal Statistical Society - Series B,  75, 345-367 with C. Francq, 2013. pdf
  23. Estimation adjusted VaR. Econometric Theory, 735-770 with C. Gouriéroux, 2013.
  24. Strict stationarity testing and estimation of explosive and stationary GARCH modelsEconometrica, 821-861, with C. Francq, 2012.
  25. QML estimation of a class of multivariate asymmetric GARCH modelsEconometric Theory, 28, 179-206, with C. Francq, 2012. 
  26. Two-stage non Gaussian QML estimation of GARCH Models and testing the efficiency of the Gaussian QMLEJournal of Econometrics, 165, 246-257, with C. Francq and G. Lepage, 2011.
  27. Merits and drawbacks of variance targeting in GARCH ModelsJournal of Financial Econometrics,   9, 619-656, with C. Francq and L. Horvath, 2011. 
  28. A conditionally heteroskedastic model with time-varying coefficients for daily gas spot pricesEnergy Economics 33, 1240-1251, with N. Regnard, 2011.
  29. Asymptotic properties of LS and QML estimators for a class of nonlinear GARCH processesJournal of Statistical Planning and Inference, 141, 488-507, with T. Hamadeh, 2011.
  30. Combining nonparametric and optimal linear time series predictionsJournal of the American Statistical Association, 105, 1554-1565, with S. Dabo and C. Francq, 2010. 
  31. Inconsistency of the MLE and inference based on weighted LS for LARCH modelsJournal of Econometrics, 159, 151-165, with C. Francq, 2010.
  32. Structure and estimation of a class of nonstationary yet non explosive GARCH models. Journal of Time Series Analysis31, 348-364,  with N.Regnard, 2010.
  33. Sup-tests for linearity in a general nonlinear AR(1) model. Econometric Theory, 26, 965-993, with C. Francq and L. Horvath, 2010.
  34. Testing the nullity of GARCH coefficients :  correction of the standard tests and relative efficiency comparisons. Journal of the American Statistical Association, 104, 313-324, with C. Francq, 2009.
  35. Bartlett's formula for a general class of nonlinear processes.  Journal of Time Series Analysis, 30, 449-465, with C. Francq, 2009.
  36. Estimating ARCH Models When the Coefficients are Allowed to be Equal to ZeroAustrian Journal of Statistics,  37, 31--40, with C. Francq, 2008.
  37. Deriving the autocovariances of powers of Markov-switching GARCH models, with applications to statistical inference. Computational Statistics and Data Analysis, 52, 3027--3046, with C. Francq, 2008.
  38. A tour in the asymptotic theory of GARCH estimationHandbook of Financial Time Series, Edts: T. G. Andersen, R.A. Davis, J-P. Kreiss, T. Mikosch, Springer Statistics, with C. Francq, 2009.
  39. A  class of stochastic unit-root bilinear processes. Mixing properties and unit-root test. Journal of Econometrics, 142, 312-326,  with C. Francq and S. Makarova, 2007.
  40. Quasi-Maximum Likelihood in GARCH processes when some coefficients are equal to zeroStochastic Processes and their Applications, 117, 1265-1284, with C. Francq, 2007.
  41. HAC estimation and strong linearity testing in weak ARMA models,  (extended version hereJournal of Multivariate Analysis, 98, 114-144, with C. Francq,  2007.
  42. Stationarity and geometric ergodicity of a class of non-linear ARCH modelsAnnals of Applied Probability, 16, 2256-2271, with Y. Saïdi, 2007.
  43. Linear-representation based estimation of stochastic volatility modelsScandinavian Journal of Statistics,  33, 785-806, with C. Francq, 2006.
  44. Mixing properties of a general class of GARCH(1,1) models without moment assumptions on the observed processEconometric Theory, 22, 815-834, with C. Francq, 2006.
  45. On Efficient Inference in GARCH Processes, in Dependence in Probability and Statistics, 305-327, Springer, edited by P. Bertail, P. Doukhan et P. Soulier, with C. Francq, 2006.
  46. The L2-Structures of Standard and Switching-regime GARCH models, Stochastic Processes and their Applications, 115, 1557-1582, with C. Francq, 2005.
  47. A central limit theorem for mixing triangular arrays of variables whose dependence is allowed to grow with the sample sizeEconometric Theory, 21, 1165-1171,  with C. Francq, 2005.
  48. Diagnostic checking in ARMA models with uncorrelated errorsJournal of the American Statistical Association, 13, 532-544,  with C. Francq and R. Roy, 2005.
  49. Recent Results for Linear Time Series Models with Non Independent Innovations. In Statistical Modeling and Analysis for Complex Data Problems, P. Duchesne and B. Rémillard Editors, Springer,  with C. Francq, 2005.
  50. Maximum Likelihood Estimation of Pure GARCH and ARMA-GARCH ProcessesBernoulli, 10, 605-637,  with C. Francq, 2004.
  51. Autocovariance Structure of Powers of Switching-regime ARMA Processes. ESAIM:Probability and Statistics,  6, 259-270, with C. Francq, 2003.
  52. Comments on the paper by Minxian Yang: "Some Properties of Vector Autoregressive Processes with Markov-Switching Coefficients". Econometric Theory, 18, 815-818, with C. Francq, 2002.
  53.  Efficient Use of High Order Autocorrelations for Estimating Autoregressive Processes. Journal of Time Series Analysis,  23, 287-312,  with C. Francq and L. Broze, 2002.
  54. Stationarity of Multivariate Markov-switching ARMA Models, Journal of Econometrics, 102, 339-364,  with C. Francq, 2001.
  55. Non Redundancy of High Order Moment Conditions for Efficient GMM Estimation of Weak AR Processes, Economic Letters, 71, 317-322, with C. Francq and L. Broze, 2001.
  56. Contemporaneous Asymmetry in GARCH Processes. Journal of Econometrics, 101, 257-294, with M. El Babsiri, 2001.
  57. Conditional Heteroskedasticity Driven by Hidden Markov Chains. Journal of Time Series Analysis,  22, 197-220,  with C. Francq and M. Roussignol, 2001.
  58. Stationnarité des modèles ARMA avec changement de régime markovien. C.R.A.S., 330, 1031-1034,  with C. Francq, 2000.
  59. Modèles ARCH avec changement de régime markovien. C.R.A.S., 330, 921-924, with C. Francq and M. Roussignol, 2000.
  60. Estimating Weak GARCH Representations. Econometric Theory, 16, 692-728,  with C. Francq, 2000.
  61. Multivariate ARMA Models with Generalized Autoregressive Linear Innovation. Stochastic Analysis and Applications, Vol. 18 n°2, 231-260,  with C. Francq, 2000.
  62. Covariance Matrix Estimation for Estimators of Mixing Weak ARMA Models. Journal of Statistical Planning and Inference, 83, 369-394,  with C. Francq, 2000.
  63. Estimation de représentations GARCH faibles. C.R.A.S., 326, 495-498,  with C. Francq, 1998.
  64. Estimation de la précision asymptotique dans l'estimation de modèles ARMA faibles. C.R.A.S., 326, 377-380,  with C. Francq, 1998.
  65. Estimating Linear Representations of Nonlinear Processes. Journal of Statistical Planning and Inference, 68, 145-165, with C. Francq, 1997.
  66. Quasi Indirect Inference for Diffusion Processes. Econometric Theory, 14, 161-186, with L. Broze and O. Scaillet, 1997.
  67. Estimation de la structure par terme des taux d'intérêt. Revue Economique, 47, 511-519, with L. Broze and O. Scaillet, 1996.
  68. Estimation de représentations ARMA faibles sous hypothèses de mélange. Comptes Rendus de l'Académie des Sciences (C.R.A.S.), 323, 297-300, with C. Francq, 1996.
  69. Testing for Continuous Time Models of the Short Term Interest Rate. Journal of Empirical Finance, 2, 199-223, with L. Broze and O. Scaillet, 1995.
  70. Modèles autorégressifs à seuils mutiples. Annales d'économie et de statistique, 36, 23-56, 1994.
  71. Estimation d'équations de diffusion à partir d'observations discrètes et de méthodes fondées sur des simulations. Cahiers du Centre d'Etude de Recherche Opérationnelle, 36, 43-55, with L. Broze and O. Scaillet, 1994.
  72. Threshold Heteroskedastic Models. Journal of Economic Dynamic and Control,  18, 931-955, 1994.
  73. Modèles Autorégressifs à un seuil. Publications de l'Institut Statistique de Paris, 85-114, 1994.
  74. Threshold ARCH models and asymmetries in volatility. Journal of Applied Econometrics, 8, 31-49, with R. Rabemananjara, 1993.
  75. Les Modèles ARCH: une revue de la littérature. Journal de la Société Statistique de Paris, 40-57, 1992. 


  1. Time Series
  2. Dynamic Models with Latent variables
  3. Financial Econometrics
  4. Risk Measures
  5. GARCH and Stochastic Volatility Models
  6. Statistics
  7. Probability and Integration,


Work in progress








Current PHD Student Supervision

Ophélie COUPERIER (joint with C. Francq and C. Hurlin), September 2017-now

Julien ROYER (joint with C. Francq), February 2019-now

Baye Matar KANDJI (joint with C. Francq), September 2020-now

Past PHD Student Supervision

Sébastien FRIES: Anticipative alpha-stable linear processes for time series analysis: conditional dynamics and estimation, 2018.

Ali AHMAD (joint with C. Francq): Contributions to the econometrics of integer-valued time series, 2016.

Guillaume LEPAGE (joint with C. Francq): Statistical inference of conditionally heteroskedastic models with stable innovations, non Gaussian contrast and misspecified volatility, 2012.

Nazim REGNARD: GARCH models with coefficients functions of an exogenous process, 2011. 

Taoufik HAMADEH (joint with C. Francq): Statistical inference in non linear GARCH models, 2010.

Yacouba B. MAINASSARA (joint with C. Francq): Estimation, validation and identification of weak vector ARMA models, 2009.

Ahmed ELGHINI (joint with C. Francq): Specification tests based on inverse autocorrelations. Asymptotic properties of inverse empirical autocorrelations, 2008. 

Hamdi RAISSI (joint with C. Francq): Contributions to the statistical inference of vector autoregressive and error-correction models, 2007. 

Antony GAUTIER (joint with C. Francq): Time-dependent coefficients time series models, 2004. 

Youssef SAIDI (joint with L. Broze): Probabilist and statistical study of non linear conditionally heteroscedastic models, 2003.





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