Granger causality
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The Granger causality test is a statistical hypothesis test for determining whether one time series is useful in forecasting another, first proposed in 1969. Ordinarily, regressions reflect “mere” correlations, but Clive Granger argued that causality in economics could be tested for by measuring the ability to predict the future values of a time series using prior values of another time series. Since the question of “true causality” is deeply philosophical, and because of the post hoc ergo propter hoc fallacy of assuming that one thing preceding another can be used as a proof of causation, econometricians assert that the Granger test finds only “predictive causality”.
A time series X is said to Granger-cause Y if it can be shown, usually through a series of t-tests and F-tests on lagged values of X (and with lagged values of Y also included), that those X values provide statistically significant information about future values of Y.
Granger defined the causality relationship based on two principles:
- The cause happens prior to its effect.
- The cause has unique information about the future values of its effect.
See also
Papers
- Granger, C. W. (1988). Some recent development in a concept of causality. Journal of econometrics, 39(1), 199-211.
- Hiemstra, C., & Jones, J. D. (1994). Testing for linear and nonlinear Granger causality in the stock price‐volume relation. The Journal of Finance, 49(5), 1639-1664.
- Barnett, L., Barrett, A. B., & Seth, A. K. (2009). Granger causality and transfer entropy are equivalent for Gaussian variables. Physical review letters, 103(23), 238701.
- Eichler, M. (2012). Causal inference in time series analysis. Causality: Statistical perspectives and applications, 327-354.
- Seth, Anil (2007). Granger causality. Scholarpedia.
- Kim, S.; Putrino, D.; Ghosh, S.; Brown, E. N. (2011). A Granger Causality Measure for Point Process Models of Ensemble Neural Spiking Activity. PLoS Comput Biol 7 (3): e1001110