The behaviour of the Lagrangian multiplier test in testing the orders of an ARMA-model (Q1084822)

Before estimating parameters in ARMA and ARMAX models it is necessary to determine the true order of the model. This can be done by the Lagrange multiplier test. The author shows that this test can exhibit some ''pathological'' behaviour, which has been overlooked in the literature. Some problems are caused by the fact that a sequence of matrices \(A_ n\) can converge to a matrix A, whereas for their ranks it may hold that \(r(A_ n)\) des not approach r(A). The consistency of an order estimation procedure can be proved using results presented in the paper.