NEARLY EFFICIENT LIKELIHOOD RATIO TESTS OF A UNIT ROOT IN AN AUTOREGRESSIVE MODEL OF ARBITRARY ORDER
研究了任意阶自回归模型中单位根假设的似然比检验的大样本性质，证明了在局部单位根渐近框架下，完全似然比检验是近有效的，其渐近局部功效函数与高斯功效包络几乎无法区分。
We study large sample properties of likelihood ratio tests of the unit-root hypothesis in an autoregressive model of arbitrary order. Earlier research on this testing problem has developed likelihood ratio tests in the autoregressive model of order 1, but resorted to a plug-in approach when dealing with higher-order models. In contrast, we consider the full model and derive the relevant large sample properties of likelihood ratio tests under a local-to-unity asymptotic framework. As in the simpler model, we show that the full likelihood ratio tests are nearly efficient, in the sense that their asymptotic local power functions are virtually indistinguishable from the Gaussian power envelopes. Extensions to sieve-type approximations and different classes of alternatives are also considered.