Diagnostic Checking in ARMA Models With Uncorrelated Errors

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Poisson QMLE of Count Time Series Models (2016, methodology): “In principle, we could thus use general diagnostic checking tools of weak ARMA models (as in Francq et al., 2005) for identifying the orders p and q of a conditional mean of the INGARCH.p; q/ form (9).”
TESTING FOR WHITE NOISE UNDER UNKNOWN DEPENDENCE AND ITS APPLICATIONS TO DIAGNOSTIC CHECKING FOR TIME SERIES MODELS (2010, methodology): “In what follows, we demonstrate that the GMC condition for the noise process in the weak ARMA respresentation can be verified for the two leading examples in Francq et al. (2005).”
Multivariate Portmanteau Test For Autoregressive Models with Uncorrelated but Nonindependent Errors (2007, background): “We are now able to state Theorem 3, which is an extension of a result given in a preliminary version of Francq et al. (2005).”
White Noise Testing and Model Diagnostic Checking for Functional Time Series (2016, methodology): “…some commonly used test statistics, such as Box and Pierce’s portmanteau test, are obtained under the i.i.d assumption, and they are no longer valid under the assumption of dependent white noise (Romano and Thombs, 1996; Lobato et al., 2002; Francq et al., 2005; Horowitz et al., 2006; Shao, 2011b).”