An Easy Way To Understand The Cross Correlation Function
Most folk have an intuitive grasp of correlation between two variables and the ubiquitous measure we use to reveal how strong this correlation is, this being Pearson's correlation coefficient a.k.a Pearson's product-moment correlation coefficient a.k.a Pearson bivariate correlation; this being denoted by the English symbol 'r' or Greek letter Rho (ρ).
When r = 1 we have perfect positive correlation which is rarely observed in nature. This occurs when two measures 'go up together' or 'go down together' such as hours of sunlight and temperature. When r = -1 we have perfect negative correlation which is again rarely observed in nature. This occurs when one measure goes up as the other goes down, this indicating an inverse relationship (a good example is a see-saw).
Between these two extremes sits r = 0, which indicates zero correlation. As a statistician I'd use an example along the lines of two sets of random numbers but we can get the same effect by considering government policies.
In the…