The value of $f_d$ reflects the correlation between measurements separated by the distance $d$ in the samples. Notice that for $d=0$, $f$ is just the sample variance, $\sigma^2$. If we divide $f_d$ by $\sigma^2$, we arrive at the so called autocorrelation function $$\begin{equation} \kappa_d = \frac{f_d}{\sigma^2} \tag{11} \end{equation}$$ which gives us a useful measure of the correlation pair correlation starting always at $1$ for $d=0$.