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Cointegration in singular ARMA models

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  • Deistler, Manfred
  • Wagner, Martin

Abstract

We consider the cointegration properties of singular ARMA processes integrated of order one. Such processes are necessarily cointegrated as opposed to the regular case. We show that in the left coprime case the cointegrating space only depends upon the autoregressive polynomial at one.

Suggested Citation

  • Deistler, Manfred & Wagner, Martin, 2017. "Cointegration in singular ARMA models," Economics Letters, Elsevier, vol. 155(C), pages 39-42.
    • Handle: RePEc:eee:ecolet:v:155:y:2017:i:c:p:39-42
    DOI: 10.1016/j.econlet.2017.03.001
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    References listed on IDEAS

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    1. Ivana Komunjer & Serena Ng, 2011. "Dynamic Identification of Dynamic Stochastic General Equilibrium Models," Econometrica, Econometric Society, vol. 79(6), pages 1995-2032, November.
    2. Bauer, Dietmar & Wagner, Martin, 2012. "A State Space Canonical Form For Unit Root Processes," Econometric Theory, Cambridge University Press, vol. 28(6), pages 1313-1349, December.
    3. Beveridge, Stephen & Nelson, Charles R., 1981. "A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the `business cycle'," Journal of Monetary Economics, Elsevier, vol. 7(2), pages 151-174.
    4. Mario Forni & Marc Hallin & Marco Lippi & Lucrezia Reichlin, 2000. "The Generalized Dynamic-Factor Model: Identification And Estimation," The Review of Economics and Statistics, MIT Press, vol. 82(4), pages 540-554, November.
    5. Anderson, Brian D.O. & Deistler, Manfred & Felsenstein, Elisabeth & Koelbl, Lukas, 2016. "The structure of multivariate AR and ARMA systems: Regular and singular systems; the single and the mixed frequency case," Journal of Econometrics, Elsevier, vol. 192(2), pages 366-373.
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    Citations

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    Cited by:

    1. Franchi, Massimo, 2018. "Testing for cointegration in I(1) state space systems via a finite order approximation," Economics Letters, Elsevier, vol. 165(C), pages 73-76.
    2. Gianluca Cubadda, 2024. "VAR models with an index structure: A survey with new results," Papers 2412.11278, arXiv.org.
    3. Lippi, Marco & Deistler, Manfred & Anderson, Brian, 2023. "High-Dimensional Dynamic Factor Models: A Selective Survey and Lines of Future Research," Econometrics and Statistics, Elsevier, vol. 26(C), pages 3-16.
    4. Massimo Franchi, 2017. "On the structure of state space systems with unit roots," DSS Empirical Economics and Econometrics Working Papers Series 2017/4, Centre for Empirical Economics and Econometrics, Department of Statistics, "Sapienza" University of Rome.
    5. Matteo Barigozzi & Marco Lippi & Matteo Luciani, 2020. "Cointegration and Error Correction Mechanisms for Singular Stochastic Vectors," Econometrics, MDPI, vol. 8(1), pages 1-23, February.

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    More about this item

    Keywords

    Cointegration; Singular ARMA systems;

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis

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