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A Parameterization of Models for Unit Root Processes: Structure Theory and Hypothesis Testing

Author

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  • Dietmar Bauer

    (Faculty of Business Administration and Economics, Bielefeld University, Universitätsstraße 25, 33615 Bielefeld, Germany)

  • Lukas Matuschek

    (Faculty of Business Administration and Economics, Bielefeld University, Universitätsstraße 25, 33615 Bielefeld, Germany
    Faculty of Statistics, TU Dortmund, Vogelpothsweg 87, 44227 Dortmund, Germany)

  • Patrick de Matos Ribeiro

    (Faculty of Business Administration and Economics, Bielefeld University, Universitätsstraße 25, 33615 Bielefeld, Germany
    Faculty of Statistics, TU Dortmund, Vogelpothsweg 87, 44227 Dortmund, Germany)

  • Martin Wagner

    (Department of Economics, University of Klagenfurt, Universitätsstraße 65-67, 9020 Klagenfurt, Austria
    Bank of Slovenia, Slovenska 35, 1505 Ljubljana, Slovenia
    Institute for Advanced Studies, Josefstädter Straße 39, 1080 Vienna, Austria)

Abstract

We develop and discuss a parameterization of vector autoregressive moving average processes with arbitrary unit roots and (co)integration orders. The detailed analysis of the topological properties of the parameterization—based on the state space canonical form of Bauer and Wagner (2012)—is an essential input for establishing statistical and numerical properties of pseudo maximum likelihood estimators as well as, e.g., pseudo likelihood ratio tests based on them. The general results are exemplified in detail for the empirically most relevant cases, the (multiple frequency or seasonal) I(1) and the I(2) case. For these two cases we also discuss the modeling of deterministic components in detail.

Suggested Citation

  • Dietmar Bauer & Lukas Matuschek & Patrick de Matos Ribeiro & Martin Wagner, 2020. "A Parameterization of Models for Unit Root Processes: Structure Theory and Hypothesis Testing," Econometrics, MDPI, vol. 8(4), pages 1-54, November.
    • Handle: RePEc:gam:jecnmx:v:8:y:2020:i:4:p:42-:d:442543
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    References listed on IDEAS

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    1. Paruolo, Paolo, 1996. "On the determination of integration indices in I(2) systems," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 313-356.
    2. Johansen, Søren & Nielsen, Morten Ørregaard, 2018. "The cointegrated vector autoregressive model with general deterministic terms," Journal of Econometrics, Elsevier, vol. 202(2), pages 214-229.
    3. Johansen, Soren, 2006. "Statistical analysis of hypotheses on the cointegrating relations in the I(2) model," Journal of Econometrics, Elsevier, vol. 132(1), pages 81-115, May.
    4. Saikkonen, Pentti & Luukkonen, Ritva, 1997. "Testing cointegration in infinite order vector autoregressive processes," Journal of Econometrics, Elsevier, vol. 81(1), pages 93-126, November.
    5. 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.
    6. Campbell, John Y., 1994. "Inspecting the mechanism: An analytical approach to the stochastic growth model," Journal of Monetary Economics, Elsevier, vol. 33(3), pages 463-506, June.
    7. Rahbek, Anders & Christian Kongsted, Hans & Jorgensen, Clara, 1999. "Trend stationarity in the I(2) cointegration model," Journal of Econometrics, Elsevier, vol. 90(2), pages 265-289, June.
    8. Zellner, Arnold & Palm, Franz, 1974. "Time series analysis and simultaneous equation econometric models," Journal of Econometrics, Elsevier, vol. 2(1), pages 17-54, May.
    9. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-1580, November.
    10. Paruolo, Paolo, 2000. "Asymptotic Efficiency Of The Two Stage Estimator In I (2) Systems," Econometric Theory, Cambridge University Press, vol. 16(4), pages 524-550, August.
    11. Juselius, Katarina, 2006. "The Cointegrated VAR Model: Methodology and Applications," OUP Catalogue, Oxford University Press, number 9780199285679.
    12. Dietmar Bauer & Martin Wagner, 2003. "On Polynomial Cointegration in the State Space Framework," Diskussionsschriften dp0313, Universitaet Bern, Departement Volkswirtschaft.
    13. Dietmar Bauer & Martin Wagner, 2005. "Autoregressive Approximations of Multiple Frequency I(1) Processes," Economics Working Papers ECO2005/09, European University Institute.
    14. Saikkonen, Pentti, 1992. "Estimation and Testing of Cointegrated Systems by an Autoregressive Approximation," Econometric Theory, Cambridge University Press, vol. 8(1), pages 1-27, March.
    15. Poskitt, D.S., 2006. "On The Identification And Estimation Of Nonstationary And Cointegrated Armax Systems," Econometric Theory, Cambridge University Press, vol. 22(6), pages 1138-1175, December.
    16. Granger, C. W. J., 1981. "Some properties of time series data and their use in econometric model specification," Journal of Econometrics, Elsevier, vol. 16(1), pages 121-130, May.
    17. Lewis, Richard & Reinsel, Gregory C., 1985. "Prediction of multivariate time series by autoregressive model fitting," Journal of Multivariate Analysis, Elsevier, vol. 16(3), pages 393-411, June.
    18. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
    19. Sims, Christopher A & Stock, James H & Watson, Mark W, 1990. "Inference in Linear Time Series Models with Some Unit Roots," Econometrica, Econometric Society, vol. 58(1), pages 113-144, January.
    20. H. Peter Boswijk & Paolo Paruolo, 2017. "Likelihood Ratio Tests of Restrictions on Common Trends Loading Matrices in I(2) VAR Systems," Econometrics, MDPI, vol. 5(3), pages 1-17, June.
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