CoViD19 Meta heuristic optimization based forecast method on time dependent bootstrapped data

Livio Fenga; Carlo Del Castello

The choice of the most appropriate resampling method is far from being an easy task, especially when the identical and independent distribution iid assumption (Efron's initial bootstrap method) is violated. Under dependence structures embedded in the data, simple sampling with replacement has been proved -see, for example Carlstein et al. (1986) -to yield suboptimal results. As a matter of fact, iid-based bootstrap schemes are not designed to capture, and therefore replicate, dependence structures. This is especially true under the actual conditions (small sample sizes and strong non-linearity). In such cases, selecting the "right" resampling scheme becomes a particularly challenging task as many resamplig schemes are not designed to capture the dynamics typically found in epidemiology. As an example, the well known resampling method called sieve bootstrap -introduced by Bühlmann et al. (1997) -cannot be employed due to the quadratic shape almost always found in this type of time series.