Granger Causality PDF

Causality versus correlation I Correlation indicates a relation between variables, but not a particular type of causality (causation) Example: correlation and causality I X (formal education level) and Y (crime rate) are negatively correlated. Possible causal structures: I X ∆ Y : th...

Causality versus correlation I Correlation indicates a relation between variables, but not a particular type of causality (causation) Example: correlation and causality I X (formal education level) and Y (crime rate) are negatively correlated. Possible causal structures: I X ∆ Y : the higher level of education causes people to find better jobs, so there is no need to engage in criminal activities I Y ∆ X: the safe area causes more people with high education levels to find the area attractive and move there I Z ∆ X, Y : a common cause Z is the public infrastructure, which causes people with high education to move there by offering high-level job opportunities, and causes a decrease in crime rates by offering an efficient police 23 Norwegian University of Life Sciences Granger causality I Granger causality is a weak causality concept in the context of time series data Concept post hoc ergo proper hoc after this, therefore because of this I If event X happens before event Y in a temporal context, and both are related (e.g., correlated) X ∆ Y is more reasonable than Y ∆ X I Granger causality does not take a third event Z into account! 24 Norwegian University of Life Sciences Granger causality I Assume events Xt and Yt on some time axis t œ T I Xt Granger causes Yt , if P (Yt |I(t ≠ 1)) ”= P (Yt |I≠X (t ≠ 1)) I I(t ≠ 1) denotes information available at time point t ≠ 1 I I≠X (t ≠ 1) denotes I(t ≠ 1) without information from X I "The probability to observe Y at time t given all information (including X) is the same as the probability to observe Y at time t given the same information excluding X" I The concept is closely related to conditional independence 25 Norwegian University of Life Sciences Granger causality I Why is this concept useful? Granger causality test I H0 : xT is not informative for predicting yT (lags of xT should not be used when predicting yt based on yt≠1 ,... ) yt = Ï0 + Ï1 B(yt ) + · · · + Ïu B u (yt ) + Át I HA : lags l1 ,... , l2 of xT are informative for predicting yT yt =Ï0 + Ï1 B(yt ) + · · · + Ïu B u (yt )+ —l1 B l1 (xt ) + · · · + —l2 B l2 (xt ) + Át 26 Norwegian University of Life Sciences Granger causality library ( vars ) library ( bruceR ) airquality _ train