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Granger causality

When time series X Granger-causes time series Y, the patterns in X are approximately repeated in Y after some time lag (two examples are indicated with arrows). Thus, past values of X can be used for the prediction of future values of Y.

The Granger causality test is a statistical hypothesis test for determining whether one time series is useful in forecasting another, first proposed in 1969.[1] 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".[2] Using the term "causality" alone is a misnomer, as Granger-causality is better described as "precedence",[3] or, as Granger himself later claimed in 1977, "temporally related".[4] Rather than testing whether X causes Y, the Granger causality tests whether X forecasts Y.[5]

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 also stressed that some studies using "Granger causality" testing in areas outside economics reached "ridiculous" conclusions.[6] "Of course, many ridiculous papers appeared", he said in his Nobel lecture.[7] However, it remains a popular method for causality analysis in time series due to its computational simplicity.[8][9] The original definition of Granger causality does not account for latent confounding effects and does not capture instantaneous and non-linear causal relationships, though several extensions have been proposed to address these issues.[8]

  1. ^ Granger, C. W. J. (1969). "Investigating Causal Relations by Econometric Models and Cross-spectral Methods". Econometrica. 37 (3): 424–438. doi:10.2307/1912791. JSTOR 1912791.
  2. ^ Diebold, Francis X. (2007). Elements of Forecasting (PDF) (4th ed.). Thomson South-Western. pp. 230–231. ISBN 978-0324359046.
  3. ^ Leamer, Edward E. (1985). "Vector Autoregressions for Causal Inference?". Carnegie-Rochester Conference Series on Public Policy. 22: 283. doi:10.1016/0167-2231(85)90035-1.
  4. ^ Granger, C. W. J.; Newbold, Paul (1977). Forecasting Economic Time Series. New York: Academic Press. p. 225. ISBN 0122951506.
  5. ^ Hamilton, James D. (1994). Time Series Analysis (PDF). Princeton University Press. pp. 306–308. ISBN 0-691-04289-6.
  6. ^ Thurman, Walter (1988). "Chickens, Eggs, and Causality or Which Came First?" (PDF). American Journal of Agricultural Economics. 70 (2): 237–238. doi:10.2307/1242062. JSTOR 1242062. Retrieved 2 April 2022.
  7. ^ Granger, Clive W. J. (2004). "Time Series Analysis, Cointegration, and Applications" (PDF). American Economic Review. 94 (3): 421–425. CiteSeerX 10.1.1.370.6488. doi:10.1257/0002828041464669. S2CID 154709108. Retrieved 12 June 2019.
  8. ^ a b Eichler, Michael (2012). "Causal Inference in Time Series Analysis" (PDF). In Berzuini, Carlo (ed.). Causality : statistical perspectives and applications (3rd ed.). Hoboken, N.J.: Wiley. pp. 327–352. ISBN 978-0470665565.
  9. ^ Seth, Anil (2007). "Granger causality". Scholarpedia. 2 (7): 1667. Bibcode:2007SchpJ...2.1667S. doi:10.4249/scholarpedia.1667.

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