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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 where n is the sample size. Explicit algebraic formulae are presented for certain special cases, including the ARMA(1,1).