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EFFICIENT LIKELIHOOD INFERENCE IN NONSTATIONARY UNIVARIATE MODELS

Published online by Cambridge University Press:  05 March 2004

Morten Ørregaard Nielsen
Morten Ørregaard Nielsen
Affiliation:
Cornell University
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Abstract

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 Gaussianity 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 tests; i.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.I am grateful to Bent Jesper Christensen, Niels Haldrup, Pentti Saikkonen (the co-editor), and two anonymous referees for many useful comments and suggestions that significantly improved this paper. This work was done while the author was at the University of Aarhus, Denmark.

Type
Research Article
Information
Econometric Theory , Volume 20 , Issue 1 , February 2004 , pp. 116 - 146
Copyright
© 2004 Cambridge University Press

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