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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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