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The role of information in nonstationary regression

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  • Patrick Marsh

Abstract

The role of standard likelihood based measures of information and efficiency is unclear when regressions involve nonstationary data. Typically the standardized score is not asymptotically Gaussian and the standardized Hessian has a stochastic, rather than deterministic limit. Here we consider a time series regression involving a deterministic covariate which can be evaporating, slowly evolving or nonstationary. It is shown that conditional information, or equivalently, profile Kullback-Leibler and Fisher Information remain informative about both the accuracy, i.e. asymptotic variance, of profile maximum likelihood estimators, as well as the power of point optimal invariant tests for a unit root. Specifically these information measures indicate fractional,rather than linear trends may minimize inferential accuracy. Such is confirmed in numerical experiment.

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  • Patrick Marsh, 2019. "The role of information in nonstationary regression," Discussion Papers 19/04, University of Nottingham, Granger Centre for Time Series Econometrics.
    • Handle: RePEc:not:notgts:19/04
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    References listed on IDEAS

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    1. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
    2. Hansen, Bruce E., 1995. "Rethinking the Univariate Approach to Unit Root Testing: Using Covariates to Increase Power," Econometric Theory, Cambridge University Press, vol. 11(5), pages 1148-1171, October.
    3. Marsh, Patrick, 2007. "The Available Information For Invariant Tests Of A Unit Root," Econometric Theory, Cambridge University Press, vol. 23(4), pages 686-710, August.
    4. Alison L. Gibbs & Francis Edward Su, 2002. "On Choosing and Bounding Probability Metrics," International Statistical Review, International Statistical Institute, vol. 70(3), pages 419-435, December.
    5. Marsh, Patrick, 2009. "The Properties Of Kullback–Leibler Divergence For The Unit Root Hypothesis," Econometric Theory, Cambridge University Press, vol. 25(6), pages 1662-1681, December.
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