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Estimation of Cointegrated Systems with I(2) Processes

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  • Kitamura, Yuichi

Abstract

This paper considers the properties of systems likelihood procedures for cointegrated systems when the I(2) variables are present. Two alternative methods are proposed: one is based on the full system likelihood, whereas another is based on the subsystem likelihood. By eliminating all unit roots in the system by the use of prior information concerning the presence of unit roots, these procedures yield estimates whose asymptotic distributions are mixed normal, free from nuisance parameters, and median-unbiased. Both methods are extensions of a full system maximum likelihood procedure by Phillips (1991a) to I(2) models. Three cases of cointegration with I(2) variables are considered in order to cover a wide variety of cointegration relationships. A triangular ECM representation and the two ML estimates are derived for each case, and the asymptotics are discussed as well. The asymptotic efficiency concerning the two estimates are considered.

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  • Kitamura, Yuichi, 1995. "Estimation of Cointegrated Systems with I(2) Processes," Econometric Theory, Cambridge University Press, vol. 11(1), pages 1-24, February.
    • Handle: RePEc:cup:etheor:v:11:y:1995:i:01:p:1-24_00
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    Cited by:

    1. Dolado, Juan J. & Marmol, Francesc, 1997. "On the properties of the Dickey-Pantula test against fractional alternatives," Economics Letters, Elsevier, vol. 57(1), pages 11-16, November.
    2. Paruolo Paolo, 2002. "Testing for common trends in conditional I(2) VAR models," Economics and Quantitative Methods qf0216, Department of Economics, University of Insubria.
    3. Engsted, Tom & Gonzalo, Jesus & Haldrup, Niels, 1997. "Testing for multicointegration," Economics Letters, Elsevier, vol. 56(3), pages 259-266, November.
    4. Cassim, Lucius, 2020. "A Residual-based Test For Multicointegration In Models With Structural Breaks And Threshold Adjustment To Steady State," MPRA Paper 101453, University Library of Munich, Germany.
    5. Paolo Paruolo & Rocco Mosconi, 2010. "Identification of cointegrating relations in I(2) vector autoregressive models," Economics and Quantitative Methods qf1007, Department of Economics, University of Insubria.
    6. Dong Shin & Man-Suk Oh, 2003. "Tests for the order of integration against higher order integration," Statistical Papers, Springer, vol. 44(3), pages 383-396, July.
    7. Mosconi, Rocco & Paruolo, Paolo, 2014. "Rank and order conditions for identification in simultaneous system of cointegrating equations with integrated variables of order two," MPRA Paper 53589, University Library of Munich, Germany.

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