| In this thesis we assess the use of subspace algorithms for the identification of nonstationary cointegrated stochastic systems. In a series of system identification experiments, the state space models obtained by subspace methods are compared with the corresponding vector autoregressive (VAR or VEC) models obtained by the popular method of Johansen.; VARMA processes are an interesting case, because a finite VAR model can not represent the underlying process exactly, while a finite state space model can do it. In our simulations we used several different VARMA data generating processes, with two or three cointegrated time series, one or two common trends, and different specifications for the trends and for the cycles. The main aspects compared were the quality of estimation of the cointegrating relations and the predictive power of the identified models.; Several subspace methods were analysed and tested, mainly the Canonical Variate Analysis (CVA or CCA) method of Larimore, and some of its variants (like the ACCA method of Bauer and Wagner, the only one which, for VARMA processes, is proved to offer consistent estimates of all the system parameters). The SSATS algorithm of Aoki was also considered.; Our results show significant differences in the quality of the identified models (subspace models vs. Johansen models), but the relative performance depends greatly on the parameters of the data generating process, and none of the methods uniformly beats the other(s). Some general features can, however, be seen. In particular, within the subspace family, none of the considered methods seem to improve the standard CCA algorithm, even though some of these methods are modifications of CCA especially designed to cope with non stationarities. |
