Boubacar Mainassara, Yacouba (2009): Multivariate portmanteau test for structural VARMA models with uncorrelated but nonindependent error terms.
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Abstract
We consider portmanteau tests for testing the adequacy of vector autoregressive movingaverage (VARMA) models under the assumption that the errors are uncorrelated but not necessarily independent. We relax the standard independence assumption to extend the range of application of the VARMA models, and allow to cover linear representations of general nonlinear processes. We first study the joint distribution of the quasimaximum likelihood estimator (QMLE) or the least squared estimator (LSE) and the noise empirical autocovariances. We then derive the asymptotic distribution of residual empirical autocovariances and autocorrelations under weak assumptions on the noise. We deduce the asymptotic distribution of the LjungBox (or BoxPierce) portmanteau statistics for VARMA models with nonindependent innovations. In the standard framework (i.e. under iid assumptions on the noise), it is known that the asymptotic distribution of the portmanteau tests is that of a weighted sum of independent chisquared random variables. The asymptotic distribution can be quite different when the independence assumption is relaxed. Consequently, the usual chisquared distribution does not provide an adequate approximation to the distribution of the BoxPierce goodnessof fit portmanteau test. Hence we propose a method to adjust the critical values of the portmanteau tests. Monte carlo experiments illustrate the finite sample performance of the modified portmanteau test.
Item Type:  MPRA Paper 

Original Title:  Multivariate portmanteau test for structural VARMA models with uncorrelated but nonindependent error terms 
Language:  English 
Keywords:  Goodnessoffit test, QMLE/LSE, BoxPierce and LjungBox portmanteau tests, residual autocorrelation, Structural representation, weak VARMA models 
Subjects:  C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables > C32  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables C  Mathematical and Quantitative Methods > C0  General > C02  Mathematical Methods C  Mathematical and Quantitative Methods > C0  General > C01  Econometrics 
Item ID:  18990 
Depositing User:  Boubacar Mainassara Yacouba 
Date Deposited:  08. Dec 2009 23:39 
Last Modified:  21. Feb 2013 03:40 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/18990 
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