Efficient Likelihold Inference in Nonstationary Univariate Models

Morten Nielsen

Economics Working Papers from Department of Economics and Business Economics, Aarhus University

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 non-standard limiting distributions that must be simulated on a case-by-case basis. However, we show that by embedding the models in a general I(d) framework the resulting estimators and tests regain all the desirable properties from standard statistical analysis. We derive the time domain maximum likelihood estimator and show that it is consistent, asymptotically normal, and under Gaussianity asymptotically efficient in the sense that it has asymptotic variance equal to the inverse of the Fisher information matrix. The three likelihood based test statistics (Wald, likelihood ratio, and Lagrange multiplier) are asymptotically equivalent and have the usual asymptotic chi-squared distribution and under the additional assumption of Gaussianity they are locally most powerful. In the special case where the dynamics of the model is characterized by a scalar parameter, we show that, in addition, the two-sided tests achieve the Gaussian power envelope of all invariant and unbiased tests, i.e. they are uniformly most powerful invariant unbiased. The finite sample properties of the tests are evaluated by Monte Carlo experiments. In contrast to what might be expected from the literature, the likelihood ratio test is found to outperform the Lagrange multiplier and Wald tests.

Keywords: Fractional Integration; Nonstationarity; Likelihood Inference; Efficient Estimation; Optimal Tests; Limiting Power; Small Sample Power (search for similar items in EconPapers)
JEL-codes: C12 C13 C22 (search for similar items in EconPapers)
Pages: 48
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Related works:
Journal Article: EFFICIENT LIKELIHOOD INFERENCE IN NONSTATIONARY UNIVARIATE MODELS (2004)
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Persistent link: https://EconPapers.repec.org/RePEc:aah:aarhec:2001-8

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