for both time series are very similar, which gives us further confidence that the model is appropriate for these data. We also
used the Akaike Information Criteria (AIC) and this resulted in a slightly more complicated model involving autoregressive
terms of orders 1, 2, 12 and 24, and moving average terms of the same orders (Table 2, Model D). The regression parameters
are again very similar to Model B, but there is only a minor improvement in AIC, indicating that the more parsimonious
Model B is preferable. Finally, to test the stability of the parameter estimates, Model B was refitted to the time series from
1950 onwards (Table 2, Model E). Again most parameters changed by only a small amount and are within the 95% confidence
intervals of the Model B parameters. The only exception to this is the autoregressive order 1 parameter which has reduced in
magnitude slightly. The reason for this is unclear, but it may reflect an improvement in the data quality over time. For this
reason we consider both Models B and E in the simulation study (see Table 2).