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This paper extends previous notions of causality to take into account the subspaces along which causality occurs as well as long run causality. The properties of these new notions of causality are extensively studied for a wide variety of time series processes. The paper then proves that the notions of stability, cointegration, and controllability can all be recast under the single framework of causality. One of the most important concepts to have risen out of the econometric time series literature has been the concept of Granger causality, first suggested by Wiener (1956) and later developed by Granger (1969).
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