Practical Methods in Multivariate Time Series Analysis (Causality, Arma, Box-Jenkins)

145 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1985.Box and Jenkins initiated the burgeoning interest in time series model building over a decade ago when they developed several specialized techniques used in model selection, estimation, and checking. These methods have been widely applied by researchers interested in lag structures, forecasts, and interrelationships of variables over time. The Box-Jenkins approach to time series analysis has proved to be quite effective when dealing with single time series, or, in certain cases, with pairs of time series. They did not, however, discuss guidelines for analysis when a bivariate or multivariate model exhibits feedback, or, in other word, when the causal relations are not unidirectional. The purpose of this thesis is to establish a workable methodology for building multivariate time series models where feedback is possible and to apply it over a range of economic data sets.The first major obstacle confronted by researchers who have ventured into a multivariate world comes in the model identification stage. The Box and Jenkins techniques that have been used so successfully in selecting the ARMA structures of single time series are not, as they stand, very useful in identifying mixed ARMA processes for models with more than one series. Some work has been done in this area but more research is needed. A major portion of this thesis entails working through a promising new approach to multivariate model specification. Parameter estimation for the model specified in the previous stage is then performed by an exact maximum likelihood algorithm. The fitted models are then subject to a series of checks to ensure that the initially specified model structure is indeed adequate. Several new model checks are presented in this thesis. One is based on a comparison of the implied model of an individual series obtained from the estimated multivariate model with the model of the same series identified and estimated alone. Also of interest is a newly developed Lagrange multiplier test which tests the hypothesis of correct specification against an alternative involving additional AR or MA terms. Finally, the issue of causality is addressed with special emphasis placed on developing and applying a Wald test of causality within the framework of multivariate ARMA models.Countless questions concerning the methodology of multivariate time series analysis still exist. It is hoped that this thesis has afforded the practical experience necessary to allow considerable insight into the properties of the various statistical tools that have been used.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD