Figure 8.3 shows the seasonal differences of the logarithm of the monthly scripts for A10 (antidiabetic) drugs sold in Australia. The transformation and differencing has made the series look relatively stationary.
To distinguish seasonal differences from ordinary differences, we sometimes refer to ordinary differences as “first differences” meaning differences at lag 1.
Sometimes it is necessary to do both a seasonal difference and a first difference to obtain stationary data, as shown in Figure 8.4. Here, the data are first transformed using logarithms (second panel). Then seasonal differenced are calculated (third panel). The data still seem a little non-stationary, and so a further lot of first differences are computed (bottom panel).