Title: Pseudo maximum likelihood analysis of multiple frequency I(1) processes: Inference on cointegrating ranks
Authors: Dietmar Bauer - University Bielefeld (Germany)
Lukas Matuschek - Technical University Dortmund (Germany) [presenting]
Patrick de Matos Ribeiro - Technical University Dortmund (Germany)
Martin Wagner - University of Klagenfurt (Austria)
Abstract: Based on an extension of the state space error correction model from the I(1) to the multiple frequency I(1) case, several test statistics are presented to determine the cointegrating ranks at the considered unit root frequencies. With multiple frequency I(1) processes we denote processes with unit roots at arbitrary frequencies with all integration orders equal to one. The considered test statistics differ whether additional parameter restrictions are imposed in a preliminary concentration step correcting for the other unit roots and stationary dynamics. However, all test statistics have the usual Brownian motion integral limiting null distributions. We complement our theoretical findings with a detailed simulation study. The most important finding is that for ARMA systems with roots close to the unit circle the state space model based test statistics outperform, in particular in small samples, previous tests calculated on autoregressive approximations with the lag lengths chosen by AIC.