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Mildly explosive autoregression under weak and strong dependence

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  • Tassos Magdalinos
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    Abstract

    A limit theory is developed for mildly explosive autoregression under both weakly and strongly dependent innovation errors. We find that the asymptotic behaviour of the sample moments is affected by the memory of the innovation process both in the in the form of the limiting distribution and, in the case of long range dependence, in the rate of convergence. However, this effect is not present in least squares regression theory as it is cancelled out by the interaction between the sample moments. As a result, the Cauchy regression theory of Phillips and Magdalinos (2007a) is invariant to the dependence structure of the innovation sequence even in the long memory case.

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    File URL: http://www.nottingham.ac.uk/economics/grangercentre/papers/08-05.pdf
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    Bibliographic Info

    Paper provided by University of Nottingham, Granger Centre for Time Series Econometrics in its series Discussion Papers with number 08/05.

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    Date of creation: May 2008
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    Handle: RePEc:not:notgts:08/05

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    Postal: School of Economics University of Nottingham University Park Nottingham NG7 2RD
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    Web page: http://www.nottingham.ac.uk/economics/grangercentre/
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    Related research

    Keywords: Central limit theory; explosive autoregression; long memory; Cauchy distribution;

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    1. L Giraitis & P C B Phillips, . "Uniform limit theory for stationary autoregression," Discussion Papers 05/23, Department of Economics, University of York.
    2. Phillips, Peter C.B. & Magdalinos, Tassos, 2007. "Limit theory for moderate deviations from a unit root," Journal of Econometrics, Elsevier, vol. 136(1), pages 115-130, January.
    3. Phillips, Peter C.B., 2007. "Regression With Slowly Varying Regressors And Nonlinear Trends," Econometric Theory, Cambridge University Press, vol. 23(04), pages 557-614, August.
    4. Giraitis, Liudas & Koul, Hira L. & Surgailis, Donatas, 1996. "Asymptotic normality of regression estimators with long memory errors," Statistics & Probability Letters, Elsevier, vol. 29(4), pages 317-335, September.
    5. Aue, Alexander & Horv th, Lajos, 2007. "A Limit Theorem For Mildly Explosive Autoregression With Stable Errors," Econometric Theory, Cambridge University Press, vol. 23(02), pages 201-220, April.
    6. Magdalinos, Tassos & Phillips, Peter C.B., 2009. "Limit Theory For Cointegrated Systems With Moderately Integrated And Moderately Explosive Regressors," Econometric Theory, Cambridge University Press, vol. 25(02), pages 482-526, April.
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