in Gourieroux-Monfort-Renault (1988); 

2. testing whether the matrix of polynomials or multilinear forms in model coefficients has than full rank or, equivalently, whether the determinant of the matrix is zero in Gourieroux-Monfort-Renault (1993); 

3. tests of Granger noncausality in VARMA models in Boudjellaba-Dufour- Roy (1992,1994); 

4. tests of noncausality at various horizons in Dufour-Renault (1998), Dufour-Pelletier-Renault (2005); 

5. tests for common factors in ARMA models in Gourieroux-Monfort- Renault (1989), Galbraith-ZindeWalsh (1997); 

6. test of volatility and covolatility in Gouri´ eroux and Jasiak (2013). 

A common feature of the above problems is the fact that the estimated asymptotic covariance matrix of the relevant nonlinear functions of coefficient estimates converges to a singular matrix on a subset of the null hypothesis – so that the usual regularity condition fails – but is non-singular (with probability one) in finite samples. The estimated covariance matrix used by the Wald- type statistic is a consistent estimator of the asymptotic covariance matrix of the corresponding nonlinear form in parameter estimates, but the rank of the estimated covariance matrix does not consistently estimate the rank of the asymptotic covariance matrix (because the rank is not a continuous function). It is important to note here that this is not an identification 

