Consider the variance of observations that are m periods apart; that is, Vm = V(yt+m – yt). A graph of Vm/V1 versus m is called a variogram. It is a nice way to check a data series for nonstationary (drifting mean) behavior. If a data series is completely uncorrelated (white noise) the variogram will always produce a plot that stays near unity. If the data series is autocorrelated but stationary, the plot of the variogram will increase for a while, but as m increases the plot of Vm/V1 will gradually stabilize and not increase any further. The plot of Vm/V1 versus m will increase without bound for nonstationary data. Apply this technique to the data in Table 12.1. Is there an indication of nonstationary behavior? Calculate the sample autocorrelation function for the data.
Compare the interpretation of both graphs.