A parameterization of models for unit root processes: Structure theory and hypothesis testing - Dietmar Bauer; Lukas Matuschek; Patrick de Matos Ribeiro; Martin Wagner (Econometrics, 2020)
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: 330; canonical form; cointegration; hypothesis testing; parameterization; state space representation; unit roots