Granger Causality Test

Conducts a Granger Causality test using the Bayesian Information Criterion to select lag length

Description

GRANGER_CAUSE is a Granger Causality Test. The null hypothesis is that the y does not Granger Cause x. A user specifies the two series, x and y, along with the significance level and the maximum number of lags to be considered. The function chooses the optimal lag length for x and y based on the Bayesian Information Criterion. The function produces the F-statistic for the Granger Causality Test along with the corresponding critical value. We reject the null hypothesis that y does not Granger Cause x if the F-statistic is greater than the critical value. Type help granger_cause to learn more.

• MATLAB release: MATLAB 7.8 (R2009a)

[Luna Bella]

I like how the author uses the Bayesian Information criterion to select the lag length which is a consistent model selection criterion

[William Gruner]

This appears to calculate the same x and y lags regardless of the actual lags present between the two vectors. In addition, the F statistic generated by the function only appears valid for specific (small) lags. The test I used involved a simple pair of sinusoids phase-shifted to various degrees with and without a small amount of Gaussian noise.

[Chandler]

William, there was a small error in the selection of the lag lengths using the BIC. It should be fixed as of 03/18/2010

[Wolfgang]

Dear Chandler, I have gratefully downloaded your script. How would it be possible to also include a stationarity check into the routine or would you recommend to check stationarity of the series beforehand? Many thanks, Wolfgang

[LangS]

This function uses Matlab function "regress" which assumes a constant term(intercept) in the linear regression and therefore violates Granger causality definition(See Granger's original paper, Econometrica 37:3 424-438, 1969).

I applied this function on two random numbers series (10 time points, lag = 2) and repeated 1000 times (every time the two series are different), and set the alpha value as 0.05. Among the 1000 tests, 400 were found to have "Granger causality"! So I think the result is not reliable.