EFFICIENT LIKELIHOOD INFERENCE IN NONSTATIONARY UNIVARIATE MODELS

Morten Ørregaard Nielsen ()

Econometric Theory, 2004, vol. 20, issue 01, pages 116-146

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.

Date: 2004
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Working Paper: Efficient Likelihold Inference in Nonstationary Univariate Models
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Persistent link: http://EconPapers.repec.org/RePEc:cup:etheor:v:20:y:2004:i:01:p:116-146_20

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