E. J. Hannan, W. T. Dunsmuir, and M. Et-deistler, Estimation of vector ARMAX models, Journal of Multivariate Analysis, vol.10, issue.3, pp.275-295, 1980.
DOI : 10.1016/0047-259X(80)90050-0

E. J. Hannan and . Et-rissanen, Recursive estimation of mixed autoregressive-moving average order, Biometrika, vol.69, issue.1, pp.81-94, 1982.
DOI : 10.1093/biomet/69.1.81

N. Herrndorf, A Functional Central Limit Theorem for Weakly Dependent Sequences of Random Variables. The Annals of Probability 12, pp.141-153, 1984.

J. R. Hosking, The Multivariate Portmanteau Statistic, Journal of the American Statistical Association, vol.15, issue.371, pp.602-608, 1980.
DOI : 10.1002/9780470316436

J. R. Hosking, Equivalent forms of the multivariate portmanteau statistic, Journal of the Royal Statistical Society B, vol.43, pp.261-262, 1981.

J. R. Hosking, Lagrange-tests of multivariate time series models, Journal of the Royal Statistical Society B, vol.43, pp.219-230, 1981.

C. M. Hurvich and C. Tsai, Regression and time series model selection in small samples, Biometrika, vol.76, issue.2, pp.297-307, 1989.
DOI : 10.1093/biomet/76.2.297

C. M. Hurvich and C. Tsai, A CORRECTED AKAIKE INFORMATION CRITERION FOR VECTOR AUTOREGRESSIVE MODEL SELECTION, Journal of Time Series Analysis, vol.6, issue.3, pp.271-279, 1993.
DOI : 10.1214/aos/1176344897

J. P. Imhof, Computing the distribution of quadratic forms in normal variables, Biometrika, vol.48, issue.3-4, pp.419-426, 1961.
DOI : 10.1093/biomet/48.3-4.419

T. Jeantheau, STRONG CONSISTENCY OF ESTIMATORS FOR MULTIVARIATE ARCH MODELS, Econometric Theory, vol.14, issue.01, pp.70-86, 1998.
DOI : 10.1017/S0266466698141038

C. Kascha, A Comparison of Estimation Methods for Vector Autoregressive Moving-Average Models. ECO Working Papers, EUI ECO, 2007.

W. K. Li and A. I. Mcleod, Distribution of the residual autocorrélations in multivariate ARMA time series models, Journal of the Royal Statistical Society B, vol.43, pp.231-239, 1981.

H. Lütkepohl, Introduction to multiple time series analysis, 1993.

H. Lütkepohl, New introduction to multiple time series analysis, 2005.
DOI : 10.1007/978-3-540-27752-1

H. Lütkepohl and H. Et-claessen, Analysis of cointegrated VARMA processes, Journal of Econometrics, vol.80, issue.2, pp.223-239, 1997.
DOI : 10.1016/S0304-4076(97)00035-3

J. R. Magnus and H. Neudecker, Matrix Differential Calculus with Applications in Statistics and Econometrics., Biometrics, vol.44, issue.4, 1988.
DOI : 10.2307/2531754

E. J. Hannan, W. T. Dunsmuir, and M. Deistler, Estimation of vector ARMAX models, Journal of Multivariate Analysis, vol.10, issue.3, pp.275-295, 1980.
DOI : 10.1016/0047-259X(80)90050-0

E. J. Hannan and R. , Recursive estimation of mixed autoregressive-moving average order, Biometrika, vol.69, issue.1, pp.81-94, 1982.
DOI : 10.1093/biomet/69.1.81

N. Herrndorf, A Functional Central Limit Theorem for Weakly Dependent Sequences of Random Variables. The Annals of Probability 12, pp.141-153, 1984.

J. P. Imhof, Computing the distribution of quadratic forms in normal variables, Biometrika, vol.48, issue.3-4, pp.419-426, 1961.
DOI : 10.1093/biomet/48.3-4.419

C. Kascha, A Comparison of Estimation Methods for Vector Autoregressive Moving-Average Models. ECO Working Papers, EUI ECO, 2007.

H. Lütkepohl, Introduction to multiple time series analysis, 1993.

H. Lütkepohl, New introduction to multiple time series analysis, 2005.
DOI : 10.1007/978-3-540-27752-1

W. K. Newey and K. D. West, A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix, Econometrica, vol.55, issue.3, pp.703-708, 1987.
DOI : 10.2307/1913610

S. Nsiri, R. , and R. , Identification of Refined ARMA Echelon Form Models for Multivariate Time Series, Journal of Multivariate Analysis, vol.56, issue.2, pp.207-231, 1996.
DOI : 10.1006/jmva.1996.0011

G. C. Reinsel, Elements of multivariate time series Analysis, 1997.

J. Rissanen and P. E. Caines, The Strong Consistency of Maximum Likelihood Estimators for ARMA Processes, The Annals of Statistics, vol.7, issue.2, pp.297-315, 1979.
DOI : 10.1214/aos/1176344615

J. L. Romano and L. A. Thombs, Inference for Autocorrelations under Weak Assumptions, Journal of the American Statistical Association, vol.85, issue.434, pp.590-600, 1996.
DOI : 10.1080/01621459.1996.10476928

H. Tong, Non-linear time series : A Dynamical System Approach, 1990.

A. W. Van-der-vaart, Asymptotic statistics, 1998.
DOI : 10.1017/CBO9780511802256

A. Wald, Note on the Consistency of the Maximum Likelihood Estimate, The Annals of Mathematical Statistics, vol.20, issue.4, pp.595-601, 1949.
DOI : 10.1214/aoms/1177729952

D. W. Andrews, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation, Econometrica, vol.59, issue.3, pp.817-858, 1991.
DOI : 10.2307/2938229

B. Mainassara, Y. Francq, and C. , Estimating structural VARMA models with uncorrelated but non-independent error terms, Working Papers, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00455673

P. J. Brockwell and R. A. Davis, Time series : theory and methods, 1991.

Y. A. Davydov, Convergence of Distributions Generated by Stationary Stochastic Processes. Theory of Probability and Applications 13, pp.691-696, 1968.

J. Dufour and D. Pelletier, Practical methods for modelling weak VARMA processes : identification, estimation and specification with a macroeconomic application, Département de sciences économiques and CIREQ, 2005.

C. Francq and H. Raïssi, Multivariate Portmanteau Test For Autoregressive Models with Uncorrelated but Nonindependent Errors, Journal of Time Series Analysis, vol.43, issue.3, pp.454-470, 2006.
DOI : 10.2307/2291655
URL : https://hal.archives-ouvertes.fr/hal-00517078

C. Francq, R. Roy, and J. Zakoïan, Diagnostic Checking in ARMA Models With Uncorrelated Errors, Journal of the American Statistical Association, vol.100, issue.470, pp.532-544, 2005.
DOI : 10.1198/016214504000001510

. Francq and J. Zakoïan, Recent Results for Linear Time Series Models with Non Independent Innovations, Statistical Modeling and Analysis for Complex Data Problems, pp.137-161, 2005.
DOI : 10.1007/0-387-24555-3_12

E. J. Hannan and R. , Recursive estimation of mixed autoregressive-moving average order, Biometrika, vol.69, issue.1, pp.81-94, 1982.
DOI : 10.1093/biomet/69.1.81

H. Lütkepohl, Introduction to multiple time series analysis, 1993.

H. Lütkepohl, New introduction to multiple time series analysis, 2005.
DOI : 10.1007/978-3-540-27752-1

J. R. Magnus and H. Neudecker, Matrix Differential Calculus with Applications in Statistics and Econometrics., Biometrics, vol.44, issue.4, 1988.
DOI : 10.2307/2531754

W. K. Newey and K. D. West, A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix, Econometrica, vol.55, issue.3, pp.703-708, 1987.
DOI : 10.2307/1913610

G. C. Reinsel, Elements of multivariate time series Analysis, 1997.

. Francq and J. Zakoïan, Recent Results for Linear Time Series Models with Non Independent Innovations, Statistical Modeling and Analysis for Complex Data Problems, pp.137-161, 2005.
DOI : 10.1007/0-387-24555-3_12

N. Herrndorf, A Functional Central Limit Theorem for Weakly Dependent Sequences of Random Variables. The Annals of Probability 12, pp.141-153, 1984.

J. R. Hosking, The Multivariate Portmanteau Statistic, Journal of the American Statistical Association, vol.15, issue.371, pp.602-608, 1980.
DOI : 10.1002/9780470316436

J. R. Hosking, Equivalent forms of the multivariate portmanteau statistic, Journal of the Royal Statistical Society B, vol.43, pp.261-262, 1981.

J. R. Hosking, Lagrange-tests of multivariate time series models, Journal of the Royal Statistical Society B, vol.43, pp.219-230, 1981.

H. Akaike, Information theory and an extension of the maximum likelihood principle, 2nd International Symposium on Information Theory, pp.267-281, 1973.

B. Mainassara, Y. Francq, and C. , Estimating structural VARMA models with uncorrelated but non-independent error terms, Working Papers, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00455673

P. J. Brockwell and R. A. Davis, Time series : theory and methods, 1991.

J. Dufour and D. Pelletier, Practical methods for modelling weak VARMA processes : identification, estimation and specification with a macroeconomic application, Département de sciences économiques and CIREQ, 2005.

D. F. Findley, The overfitting principles supporting AIC, 1993.

C. Francq and H. Raïssi, Multivariate Portmanteau Test For Autoregressive Models with Uncorrelated but Nonindependent Errors, Journal of Time Series Analysis, vol.43, issue.3, pp.454-470, 2006.
DOI : 10.2307/2291655
URL : https://hal.archives-ouvertes.fr/hal-00517078

C. Francq, R. Roy, and J. Zakoïan, Diagnostic Checking in ARMA Models With Uncorrelated Errors, Journal of the American Statistical Association, vol.100, issue.470, pp.532-544, 2005.
DOI : 10.1198/016214504000001510

. Francq and J. Zakoïan, Estimating linear representations of nonlinear processes, Journal of Statistical Planning and Inference, vol.68, issue.1, pp.145-165, 1998.
DOI : 10.1016/S0378-3758(97)00139-0

. Francq and J. Zakoïan, Covariance matrix estimation for estimators of mixing weak ARMA models, Journal of Statistical Planning and Inference, vol.83, issue.2, pp.369-394, 2000.
DOI : 10.1016/S0378-3758(99)00109-3

. Francq and J. Zakoïan, Recent Results for Linear Time Series Models with Non Independent Innovations, Statistical Modeling and Analysis for Complex Data Problems, pp.137-161, 2005.
DOI : 10.1007/0-387-24555-3_12

. Francq and J. Zakoïan, HAC estimation and strong linearity testing in weak ARMA models, Journal of Multivariate Analysis, vol.98, issue.1, pp.114-144, 2007.
DOI : 10.1016/j.jmva.2006.02.003

E. J. Hannan and R. , Recursive estimation of mixed autoregressive-moving average order, Biometrika, vol.69, issue.1, pp.81-94, 1982.
DOI : 10.1093/biomet/69.1.81

C. M. Hurvich and C. Tsai, Regression and time series model selection in small samples, Biometrika, vol.76, issue.2, pp.297-307, 1989.
DOI : 10.1093/biomet/76.2.297

C. M. Hurvich and C. Tsai, A CORRECTED AKAIKE INFORMATION CRITERION FOR VECTOR AUTOREGRESSIVE MODEL SELECTION, Journal of Time Series Analysis, vol.6, issue.3, pp.271-279, 1993.
DOI : 10.1214/aos/1176344897

H. Lütkepohl, Introduction to multiple time series analysis, 1993.

H. Lütkepohl, New introduction to multiple time series analysis, 2005.
DOI : 10.1007/978-3-540-27752-1

J. R. Magnus and H. Neudecker, Matrix Differential Calculus with Applications in Statistics and Econometrics., Biometrics, vol.44, issue.4, 1988.
DOI : 10.2307/2531754

G. C. Reinsel, Elements of multivariate time series, 1993.

G. C. Reinsel, Elements of multivariate time series Analysis, 1997.

J. L. Romano and L. A. Thombs, Inference for Autocorrelations under Weak Assumptions, Journal of the American Statistical Association, vol.85, issue.434, pp.590-600, 1996.
DOI : 10.1080/01621459.1996.10476928