For this chapter, this is where I think the rubber meets the road and we'll separate causality from mere correlation—well, statistically speaking, anyway. This isn't the first time that this technique has been applied to the problem. Triacca (2005) found no evidence to suggest that atmospheric CO2 Granger caused the surface temperature anomalies. On the other hand, Kodra (2010) concluded that there's a causal relationship, but put forth the caveat that their data wasn't stationary even after a second-order differencing. While this effort won't settle the debate, it'll hopefully inspire you to apply the methodology in your personal endeavors. The topic at hand certainly provides an effective training ground to demonstrate the Granger causality. 

Our plan here is to first demonstrate spurious linear regression where the residuals suffer from autocorrelation, also known as serial correlation. Then, we'll examine two different approaches to Granger causality. The first will be the traditional methods, where both series are stationary. Then, we'll look at the method demonstrated by Toda and Yamamoto (1995), which applies the methodology to the raw data or, as it's sometimes called, the levels.