Investigating causal relations by econometric models and cross-spectral methods. (English) Zbl 1366.91115

Granger, C. W. J.

Econometrica 37, 424-438 (1969).

Summary: There occurs on some occasions a difficulty in deciding the direction of causality between two related variables and also whether or not feedback is occurring. Testable definitions of causality and feedback are proposed and illustrated by use of simple two-variable models. The important problem of apparent instantaneous causality is discussed and it is suggested that the problem often arises due to slowness in recording information or because a sufficiently wide class of possible causal variables has not been used. It can be shown that the cross spectrum between two variables can be decomposed into two parts, each relating to a single causal arm of a feedback situation. Measures of causal lag and causal strength can then be constructed. A generalisation of this result with the partial cross spectrum is suggested.

MSC:

62P20	Applications of statistics to economics
62M10	Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M15	Inference from stochastic processes and spectral analysis
91B84	Economic time series analysis