An asymptotic expansion for the distribution of the likelihood radio criterion for a gaussian autoregressive moving average process under a local alternative

In this paper, we shall derive the asymptotic expansion for the distribution of the likelihood ratio criterion for a Gaussian autoregressive moving average process under a sequence of local alternative hypotheses converging to the null hypothesis with rate of convergence [formula omitted] where n is the sample size. Explicit algebraic formulae are presented for certain special cases, including the ARMA(1,1).