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

Dietmar Bauer, Lukas Matuschek, Patrick de Matos Ribeiro and Martin Wagner
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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
Patrick de Matos Ribeiro: Faculty of Business Administration and Economics, Bielefeld University, Universitätsstraße 25, 33615 Bielefeld, Germany

Econometrics, 2020, vol. 8, issue 4, 1-54

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.

Keywords: canonical form; cointegration; hypothesis testing; parameterization; state space representation; unit roots (search for similar items in EconPapers)
JEL-codes: B23 C C00 C01 C1 C2 C3 C4 C5 C8 (search for similar items in EconPapers)
Date: 2020
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