The reason for the poor model fit is not clear. A contributing
factor might be that the time series are nonstationary:
visual inspection of Figures four and five in
(Bonsall et al. 2012) shows a variation in mean for some
of the time plots. To mitigate non-stationarity, a common
technique is to difference the time series, as in ARIMA
modelling, or to use a technique that has the equivalent
effect, such as simple exponential smoothing.