Further Generalizations of Cointegration: Modeling Many Variables and Introducing Repellors

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This project makes an important contribution to the statistical theory of the analysis of economic time series. It represents a continuation of earlier work on cointegration, which is a way to capture equilibrium relations among dynamic variables. A vector time series xt is said to be cointegrated if a linear combination of the levels of the elements of xt is stationary with finite variance. Much empirical research in macroeconomics has shown that economic time series data typically include non-stationary processes such as trends and are therefore linked together in the long run. To gain any meaningful insight into the actual movements of the variable in the economy, they must be purged of the influence of the non-stationary processes. Cointegration is a way of doing this since the linear combinations of the levels of time series variables are stationary, even if the underlying series are not. In prior work, the linear combination is an attractor for the levels of the series. The extension of these concepts in this project involve the concept of a repellor, which is a region in the phase space, away from which xt is relatively likely to move. The concept of a negative strength of attraction is developed for a repellor. Both attractors and repellors are related to stable and unstable equilibria in deterministic models and the work in this project will develop statistical tests for their presence. The goal is to provide a more general set of tools for studying short memory economic processes, through attractors and varying strength of attraction; and for modelling long memory processes, including trends, with repellors. A second part of the project involves work on the dimensionality problems in linear systems of cointegrated time series. The economy is divided into sectors and a common vector of each sector is estimated and analyzed. This will allow for an analysis with many fewer variables than if all of the series are considered jointly.