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Linear vs. Log‐linear Unit‐Root Specification: An Application of Mis‐specification Encompassing

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  • Aris Spanos
  • David F. Hendry
  • J. James Reade

Abstract

The objective of this paper is to apply the mis‐specification (M‐S) encompassing perspective to the problem of choosing between linear and log‐linear unit‐root models. A simple M‐S encompassing test, based on an auxiliary regression stemming from the conditional second moment, is proposed and its empirical size and power are investigated using Monte Carlo simulations. It is shown that by focusing on the conditional process the sampling distributions of the relevant statistics are well behaved under both the null and alternative hypotheses. The proposed M‐S encompassing test is illustrated using US total disposable income quarterly data.

Suggested Citation

  • Aris Spanos & David F. Hendry & J. James Reade, 2008. "Linear vs. Log‐linear Unit‐Root Specification: An Application of Mis‐specification Encompassing," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(s1), pages 829-847, December.
    • Handle: RePEc:bla:obuest:v:70:y:2008:i:s1:p:829-847
    DOI: 10.1111/j.1468-0084.2008.00532.x
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    References listed on IDEAS

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    1. Maozu Lu & Grayham E. Mizon & Chiara Monfardini, 2008. "Simulation Encompassing: Testing Non‐nested Hypotheses," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(s1), pages 781-806, December.
    2. Hendry, David F. & Richard, Jean-Francois, 1982. "On the formulation of empirical models in dynamic econometrics," Journal of Econometrics, Elsevier, vol. 20(1), pages 3-33, October.
    3. Mizon, Grayham E & Richard, Jean-Francois, 1986. "The Encompassing Principle and Its Application to Testing Non-nested Hypotheses," Econometrica, Econometric Society, vol. 54(3), pages 657-678, May.
    4. Spanos,Aris, 1999. "Probability Theory and Statistical Inference," Cambridge Books, Cambridge University Press, number 9780521424080.
    5. Spanos,Aris, 1986. "Statistical Foundations of Econometric Modelling," Cambridge Books, Cambridge University Press, number 9780521269124, January.
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    1. Luigi Ermini & David F. Hendry, 2008. "Log Income vs. Linear Income: An Application of the Encompassing Principle," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(s1), pages 807-827, December.
    2. Maozu Lu & Grayham E. Mizon & Chiara Monfardini, 2008. "Simulation Encompassing: Testing Non‐nested Hypotheses," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(s1), pages 781-806, December.
    3. Masayoshi Hayashi, 2013. "On the Decomposition of Regional Stabilization and Redistribution," CIRJE F-Series CIRJE-F-910, CIRJE, Faculty of Economics, University of Tokyo.
    4. Katarina Juselius & Niels Framroze Møller & Finn Tarp, 2014. "The Long-Run Impact of Foreign Aid in 36 African Countries: Insights from Multivariate Time Series Analysis," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 76(2), pages 153-184, April.
    5. Jennifer L. Castle & Jurgen A. Doornik & David Hendry, 2019. "Some forecasting principles from the M4 competition," Economics Papers 2019-W01, Economics Group, Nuffield College, University of Oxford.

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