This paper proposes a generalised Wald type tests to
test the hypothesis of the nonlinear restrictions. We circumvent the problem of
singularity of the covariance matrix associated with the usual Wald test by
proposing a generalised inverse procedure, and an alternative simple procedure
which can be approximated by a suitable chi-square distribution. New threshold
value is derived to estimate the rank of the covariance matrix.
Ratsimalahelo, Z. (2001) Specification of VARMA Echelon Form Models. In: Neck, R. Eds., Proceedings IFAC in Symposium on Modelling and Control of Economic Systems, Elsevier, Pergamon Press, 129-137. https://doi.org/10.1016/S1474-6670(17)33052-5
Lardies, J. and Ratsimalahelo, Z. (2005) Model Order Estimation of Multivariable Stochastic Process. Communications in Statistics-Simulation and Computation, 34, 863-877. https://doi.org/10.1080/03610910500308123