contrary to what Perretti et al. (2013b,c) and Hartig and Dormann
(2013) did, predictive time series were not launched from the true
population sizes X(t), but from a maximum-likelihood estimator of
the current population size. This choice ensures a more realistic
setting where only past observed population sizes N(t) are known.
Also note that it would have been possible to use as starting values for
the validation time series the sampled MCMC values for the true
population sizes X(t), but it would have implied to repeat the
parametric fitting for each starting value of the validation time series,
which would have been here prohibitively costly computationally.
Overall forecasting efficiency was summarized in the statistics
AreaSRMSE defined as the overall improvement of the forecast compared
to a forecast equal to the average population size (having a
SRMSE equal to 1). AreaSRMSE was computed as: AreaSRMSE ¼ Σ 8
i ¼ 1 maxð1SRMSEðiÞ; 0Þ where SRMSE(i) is the SRMSE of a forecast
i time steps in the future. Negative values for 1SRMSE(i) were not
considered in this formula to focus on the short-term forecast
efficiency of the parametric and nonparametric methods, since both
will fail for long-term predictions in chaotic systems (Perretti et al.,
2013b).