*"Granger causality is a standard linear technique for determining whether one time series is useful in forecasting another."*(Irwin and Sanders, 2011).

A series 'granger' causes another series if it consistently predicts it. If series X granger causes Y, while we can't be certain that this relationship is causal in any rigorous way, we might be fairly certain that Y doesn't cause X.

Example:

Yt = B0 + B1*Yt-1 +... Bp*Yt-p + A2*Xt-1+.....+Ap*Xt-p + Et

if we reject the hypothesis that all the 'A' coefficients jointly = 0 then 'X' granger causes 'Y'

Xt = B0 + B1*Xt-1 +... Bp*Xt-p + A2*Yt-1+.....+Ap*Yt-p + Et

if we reject the hypothesis that all the 'A' coefficients jointly = 0 then 'Y' granger causes 'X'

**Applications:**

Below are some applications where granger causality methods were used to test the impacts of index funds on commodity market price and volatility.

The Impact of Index Funds in Commodity Futures Markets:A Systems Approach

DWIGHT R. SANDERS AND SCOTT H. IRWIN

The Journal of Alternative Investments

Summer 2011, Vol. 14, No. 1: pp. 40-49

Irwin, S. H. and D. R. Sanders (2010), “The Impact of Index and Swap Funds on Commodity Futures Markets: Preliminary Results”, OECD Food, Agriculture and Fisheries Working Papers, No. 27, OECD Publishing. doi: 10.1787/5kmd40wl1t5f-en

Index Trading and Agricultural Commodity Prices:

A Panel Granger Causality Analysis

Gunther Capelle-Blancard and Dramane Coulibaly

CEPII, WP No 2011 – 28

No 2011 – 28

December

**References:**

Using Econometrics: A Practical Guide (6th Edition) A.H. Studenmund. 2011

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