Estimating structural VARMA models with uncorrelated but non-independent error terms
AbstractThe asymptotic properties of the quasi-maximum likelihood estimator (QMLE) of vector autoregressive moving-average (VARMA) models are derived under the assumption that the errors are uncorrelated but not necessarily independent. Relaxing the independence assumption considerably extends the range of application of the VARMA models, and allows to cover linear representations of general nonlinear processes. Conditions are given for the consistency and asymptotic normality of the QMLE. A particular attention is given to the estimation of the asymptotic variance matrix, which may be very different from that obtained in the standard framework. Modified versions of the Wald, Lagrange Multiplier and Likelihood Ratio tests are proposed for testing linear restrictions on the parameters.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 15141.
Date of creation: 2009
Date of revision:
Echelon form; Lagrange Multiplier test; Likelihood Ratio test; Nonlinear processes; QMLE; Structural representation; VARMA models; Wald test.;
Other versions of this item:
- Boubacar Mainassara, Y. & Francq, C., 2011. "Estimating structural VARMA models with uncorrelated but non-independent error terms," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 102(3), pages 496-505, March.
- C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-05-16 (All new papers)
- NEP-ECM-2009-05-16 (Econometrics)
- NEP-ETS-2009-05-16 (Econometric Time Series)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Francq, Christian & ZakoÃ¯an, Jean-Michel, 2007. "HAC estimation and strong linearity testing in weak ARMA models," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 98(1), pages 114-144, January.
- Duchesne, Pierre & Roy, Roch, 2004. "On consistent testing for serial correlation of unknown form in vector time series models," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 89(1), pages 148-180, April.
- Whitney K. Newey & Kenneth D. West, 1986.
"A Simple, Positive Semi-Definite, Heteroskedasticity and AutocorrelationConsistent Covariance Matrix,"
NBER Technical Working Papers
0055, National Bureau of Economic Research, Inc.
- Newey, Whitney K & West, Kenneth D, 1987. "A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix," Econometrica, Econometric Society, Econometric Society, vol. 55(3), pages 703-08, May.
- Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Publishing House "SINERGIA PRESS", Publishing House "SINERGIA PRESS", vol. 33(1), pages 125-132.
- Findley, David F. & Potscher, Benedikt M. & Wei, Ching-Zong, 2004. "Modeling of time series arrays by multistep prediction or likelihood methods," Journal of Econometrics, Elsevier, Elsevier, vol. 118(1-2), pages 151-187.
- Francq, Christian & Roy, Roch & Zakoian, Jean-Michel, 2005. "Diagnostic Checking in ARMA Models With Uncorrelated Errors," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 100, pages 532-544, June.
- Kohn, R, 1979. "Asymptotic Estimation and Hypothesis Testing Results for Vector Linear Time Series Models," Econometrica, Econometric Society, Econometric Society, vol. 47(4), pages 1005-30, July.
- Andrews, Donald W K, 1991.
"Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation,"
Econometrica, Econometric Society,
Econometric Society, vol. 59(3), pages 817-58, May.
- Donald W.K. Andrews, 1988. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
- Francq, Christian & Zako an, Jean-Michel, 2000.
"Estimating Weak Garch Representations,"
Econometric Theory, Cambridge University Press,
Cambridge University Press, vol. 16(05), pages 692-728, October.
- Christian Francq & Jean-Michel ZakoÃ¯an, 1997. "Estimating Weak Garch Representations," Working Papers, Centre de Recherche en Economie et Statistique 97-40, Centre de Recherche en Economie et Statistique.
- Nsiri, SaÃ¯d & Roy, Roch, 1996. "Identification of Refined ARMA Echelon Form Models for Multivariate Time Series," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 56(2), pages 207-231, February.
- Christian Francq & Hamdi RaÃ¯ssi, 2007. "Multivariate Portmanteau Test For Autoregressive Models with Uncorrelated but Nonindependent Errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(3), pages 454-470, 05.
- Hannan, E. J. & Dunsmuir, W. T. M. & Deistler, M., 1980. "Estimation of vector ARMAX models," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 10(3), pages 275-295, September.
- Christian Kascha, 2007. "A Comparison of Estimation Methods for Vector Autoregressive Moving-Average Models," Economics Working Papers, European University Institute ECO2007/12, European University Institute.
- Tucker McElroy & Michael W. McCracken, 2012. "Multi-step ahead forecasting of vector time series," Working Papers, Federal Reserve Bank of St. Louis 2012-060, Federal Reserve Bank of St. Louis.
- Boubacar Mainassara, Yacouba, 2009. "Multivariate portmanteau test for structural VARMA models with uncorrelated but non-independent error terms," MPRA Paper 18990, University Library of Munich, Germany.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ekkehart Schlicht).
If references are entirely missing, you can add them using this form.