Testing for Granger Causality

1
Testing for Granger Causality

• Suppose you have two time-series
• xt
• yt
• Your objective is to find out whether xt is
  useful in predicting future values of yt.
• One way to do this is to test for Granger
  Causality.

2
Testing for Granger Causality

• A test for Granger causality asks the following
  question
• Can you predict yt better using past values of
  both yt and xt than just past yt?
• If the answer to this question is yes. Than we
  say that xt Granger causes yt.

3
Granger Causality Tests in Practice

• To test for Granger causality we would run two
  regressions an unrestricted regression and a
  restricted regression
• regress yt on its own lagged values and on lagged
  values of xt.
• Regress yt on only its own lagged values.

4
Granger Causality Tests

• Using the residual sum of squares from the
  restricted and unrestricted regressions we can
  test the hypothesis that the coefficients on the
  lags of xt are zero.
• This is very easy to do in Matlab using the
  Matlab commands
• res var(y,nlag) estimates var
• cutoff 0.1 sets 90 confidence interval
• for Granger Causality tests
• pgranger(res,vname,cutoff) prints p-values

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Granger Causality test outputNaN means var in
col GC var in row