Recent literature shows that embedding fractionally integrated time series models with spectral poles at the long-run and/or seasonal frequencies in autoregressive frameworks leads to estimators and test statistics with nonstandard limiting distributions.However,we demonstrate that when embedding such models in a general I(d) framework the resulting estimators and tests regain desirable properties from standard statistical analysis.We show the existence of a local time domain maximum likelihood estimator and its asymptotic normality-and under Gauss-ianity asymptotic efficiency.The Wald,likelihood ratio,and Lagrange multiplier tests are asymptotically equivalent and chi-squared distributed under local alternatives.With independent and identically distributed Gaussian errors and a scalar parameter,we show that the tests in addition achieve the asymptotic Gaussian power envelope of all invariant unbiased testsi.e.,they are asymptotically uniformly most powerful invariant unbiased against local alternatives.In a Monte Carlo study we document the finite sample superiority of the likelihood ratio test.
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