The portmanteau test is a widely used diagnostic tool for univariate and multivariate time-series models. Its asymptotic distribution is known for the unconstrained vector autoregressive moving-average (VARMA) case and for VAR models with constraints on the autoregressive coefficients. In this article, we give conditions under which the test can be applied to constrained VARMA models. Unfortunately, it cannot generally be applied to models with constraints that simultaneously affect the ARMA polynomial coefficients and the covariance matrix of the innovations (mixing constraints). This happens in latent-variable models such as dynamic factor models (DFM). In addition, when there are constraints on the covariance matrix it seems convenient to check the goodness of fit using the zero-lag residual covariances. We propose an extended portmanteau test that not only checks the autocorrelations of the residuals but also whether their covariance matrix is consistent with the constraints. We prove that the statistic is asymptotically distributed as a chi-square for ARMA models under the assumption that the innovations have Gaussian-like fourth-order moments. We also show that the test is appropriate for the DFM, Peña-Box model and factor-structural vector autoregression (FSVAR). Copyright 2008 The Author. Journal compilation 2008 Blackwell Publishing Ltd
Download Info
To download:
If you experience problems downloading a file, check if you have the
proper application to
view it first. Information about this may be contained
in the File-Format links below. 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.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.