four tests for granger non causality of 2 timeseries
all four tests give similar results params_ftest and ssr_ftest are equivalent based on F test which is identical to lmtest:grangertest in R
x : array, 2d, (nobs,2)
maxlag : integer
verbose : bool
results : dictionary
TODO: convert to class and attach results properly
The Null hypothesis for grangercausalitytests is that the time series in the second column, x2, does NOT Granger cause the time series in the first column, x1. Grange causality means that past values of x2 have a statistically significant effect on the current value of x1, taking past values of x1 into account as regressors. We reject the null hypothesis that x2 does not Granger cause x1 if the pvalues are below a desired size of the test.
The null hypothesis for all four test is that the coefficients corresponding to past values of the second time series are zero.
‘params_ftest’, ‘ssr_ftest’ are based on F distribution
‘ssr_chi2test’, ‘lrtest’ are based on chi-square distribution
http://en.wikipedia.org/wiki/Granger_causality Greene: Econometric Analysis