title: statsmodel package grangercausalitytests output explanation?
body: <p>I'm currently doing a project where I'm trying to find evidence of causality between human activity and global warming. I've been trying to run a granger causality test of annual emissions on global temperature after differencing both variables and checking for unit roots.</p>
  
  <pre><code>test = pd.DataFrame({'temp':temperature,'emissions':emissions)
  sm.tsa.stattools.grangercausalitytests(test,30)
  </code></pre>
  
  <p>Can somebody help me make more sense of the output given?</p>
  
  <p>Sample Output for Lag 11 and 14:</p>
  
  <pre><code>Granger Causality
  number of lags (no zero) 11
  ssr based F test:         F=1.1019  , p=0.3716  , df_denom=76, df_num=11
  ssr based chi2 test:   chi2=15.7887 , p=0.1492  , df=11
  likelihood ratio test: chi2=14.6493 , p=0.1991  , df=11
  parameter F test:         F=1.1019  , p=0.3716  , df_denom=76, df_num=11
  
  ...
  number of lags (no zero) 14
  ssr based F test:         F=1.2862  , p=0.2394  , df_denom=67, df_num=14
  ssr based chi2 test:   chi2=25.8004 , p=0.0274  , df=14
  likelihood ratio test: chi2=22.8514 , p=0.0627  , df=14
  parameter F test:         F=1.2862  , p=0.2394  , df_denom=67, df_num=14
  </code></pre>
  
  <p>When would the Chi-squared test results be preferable to the F test? I was under the impression that Chi-squared is preferred with higher lag number, but the original sample size is pretty small ( n = 100).</p>
  
  <p>If the null hypothesis of the test is no granger causality, I'm guessing that there under the chi-squared test, emissions 'granger causes' global warming at a 95% CI at lag 14? Please correct me if I'm wrong.</p>