Efficient Likelihood Inference in Nonstationary Univariate Models

U of Aarhus, Economics Working Paper No. 2001-8

39 Pages Posted: 29 Oct 2001

Date Written: April 23, 2002


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.

JEL Classification: C12, C13, C22

Suggested Citation

Nielsen, Morten Orregaard, Efficient Likelihood Inference in Nonstationary Univariate Models (April 23, 2002). U of Aarhus, Economics Working Paper No. 2001-8. Available at SSRN: https://ssrn.com/abstract=288842 or http://dx.doi.org/10.2139/ssrn.288842

Morten Orregaard Nielsen (Contact Author)

Queen's University - Department of Economics ( email )

94 University Avenue
Kingston K7L 3N6, Ontario

HOME PAGE: http://www.econ.queensu.ca/faculty/nielsen/

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