Testing for serial correlation of unknown form in cointegrated time series models |
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Authors: | Pierre Duchesne |
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Institution: | (1) Département de mathématiques et de statistique, Université de Montréal, Succursale Centre-Ville, CP 6128, H3C 3J7 Montréal, Québec, Canada |
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Abstract: | Portmanteau test statistics are useful for checking the adequacy of many time series models. Here we generalized the omnibus
procedure proposed by Duchesne and Roy (2004,Journal of Multivariate Analysis,89, 148–180) for multivariate stationary autoregressive models with exogenous variables (VARX) to the case of cointegrated (or
partially nonstationary) VARX models. We show that for cointegrated VARX time series, the test statistic obtained by comparing
the spectral density of the errors under the null hypothesis of non-correlation with a kernel-based spectral density estimator,
is asymptotically standard normal. The parameters of the model can be estimated by conditional maximum likelihood or by asymptotically
equivalent estimation procedures. The procedure relies on a truncation point or a smoothing parameter. We state conditions
under which the asymptotic distribution of the test statistic is unaffected by a data-dependent method. The finite sample
properties of the test statistics are studied via a small simulation study. |
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Keywords: | Vector autoregressive process cointegration exogenous variables kernel spectrum estimator diagnostic test portmanteau test |
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