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Modeling I(2) Processes Using Vector Autoregressions Where the Lag Length Increases with the Sample Size
Article

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

1
Faculty of Business Administration and Economics, Bielefeld University, Universitätsstraße 25, 33615 Bielefeld, Germany
2
Faculty of Statistics, TU Dortmund, Vogelpothsweg 87, 44227 Dortmund, Germany
3
Department of Economics, University of Klagenfurt, Universitätsstraße 65-67, 9020 Klagenfurt, Austria
4
Bank of Slovenia, Slovenska 35, 1505 Ljubljana, Slovenia
5
Institute for Advanced Studies, Josefstädter Straße 39, 1080 Vienna, Austria
*
Author to whom correspondence should be addressed.
Received: 18 April 2018 / Revised: 3 November 2020 / Accepted: 4 November 2020 / Published: 10 November 2020
(This article belongs to the Special Issue Celebrated Econometricians: Katarina Juselius and Søren Johansen)
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. View Full-Text
Keywords: canonical form; cointegration; hypothesis testing; parameterization; state space representation; unit roots canonical form; cointegration; hypothesis testing; parameterization; state space representation; unit roots
MDPI and ACS Style

Bauer, D.; Matuschek, L.; de Matos Ribeiro, P.; Wagner, M. A Parameterization of Models for Unit Root Processes: Structure Theory and Hypothesis Testing. Econometrics 2020, 8, 42. https://0-doi-org.brum.beds.ac.uk/10.3390/econometrics8040042

AMA Style

Bauer D, Matuschek L, de Matos Ribeiro P, Wagner M. A Parameterization of Models for Unit Root Processes: Structure Theory and Hypothesis Testing. Econometrics. 2020; 8(4):42. https://0-doi-org.brum.beds.ac.uk/10.3390/econometrics8040042

Chicago/Turabian Style

Bauer, Dietmar, Lukas Matuschek, Patrick de Matos Ribeiro, and Martin Wagner. 2020. "A Parameterization of Models for Unit Root Processes: Structure Theory and Hypothesis Testing" Econometrics 8, no. 4: 42. https://0-doi-org.brum.beds.ac.uk/10.3390/econometrics8040042

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