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Title: Pseudo maximum likelihood analysis of I(2) processes in the state space framework Authors:  Lukas Matuschek - Technical University Dortmund (Germany) [presenting]
Dietmar Bauer - University Bielefeld (Germany)
Patrick de Matos Ribeiro - Technical University Dortmund (Germany)
Martin Wagner - University of Klagenfurt (Austria)
Abstract: Nominal macroeconomic time series are regularly found to be adequately described as $I(2)$ processes, with cointegration analysis typically performed in the vector autoregressive (VAR) framework. The VAR framework may be too restrictive: First, VAR processes are not closed under marginalization or aggregation, where in both cases the resulting processes are in general vector autoregressive moving average (VARMA) processes. Second, the solutions of dynamic stochastic economic models are typically VARMA processes rather than VAR processes. To overcome the limitation to VAR processes we develop estimation and inference techniques for $I(2)$ cointegrated VARMA processes cast in state space format. In particular we derive consistency as well as the asymptotic distributions of estimators maximizing the Gaussian pseudo likelihood function. As usual, the parameters corresponding to $I(2)$ and $I(1)$ variables are estimated super-consistently at rates $T^2$ and $T$ respectively, whereas all other parameters are estimated at rate $T^{1/2}$. The limiting distributions of the parameters corresponding to the integrated components are mixtures of Brownian motions, the parameters of the stationary subsystem are asymptotically normally distributed. Furthermore, we discuss hypothesis tests for the cointegrating ranks as well as for the cointegrating spaces.