Title: Pseudo maximum likelihood analysis of multiple frequency I(1) processes: Parameter estimation
Authors: Dietmar Bauer - University Bielefeld (Germany)
Lukas Matuschek - Technical University Dortmund (Germany)
Patrick de Matos Ribeiro - Technical University Dortmund (Germany) [presenting]
Martin Wagner - University of Klagenfurt (Austria)
Abstract: The aim is to derive the asymptotic properties, consistency and the asymptotic distribution, of pseudo maximum likelihood parameter estimators for multiple frequency I(1) processes considered in the state space framework. With multiple frequency I(1) processes we denote processes with unit roots at arbitrary frequencies with integration orders all equal to one. As usual, the parameters corresponding to the nonstationary components are estimated super-consistently at rate T, whereas all other parameters are estimated at rate square root of T. The limiting distributions are mixtures of Brownian motions and normal distributions, respectively. Our simulation results indicate that for systems with unit roots at several frequencies pseudo maximum likelihood estimation leads to more precise estimates of the cointegrating spaces and to better predictions than subspace estimation of the state space systems or reduced rank regression of autoregressive approximations.