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 \( d=0 \).