Scenario generation using historical data paths

There are situations where it is required that the generated scenarios consists of actual data points or sequences from historical data. For example, users of the optimization model may feel more confidence if the model uses ‘real’ data, instead of synthetic ones. Moreover, using historical sequences ensures correct dependencies both between variables and in time—these would otherwise have to be captured in some way. In this context, we have to distinguish two situations: in one, we have historical data and want to generate scenarios from the historical distribution, or possibly some subset of it, such as only winter or only week days. This is typical for long-term models that are not used operationally. For example, such series are employed in the TIMES (Loulou and Lettila, 2016; Loulou et al., 2016) and EMPIRE (Skar et al., 2016) energy models. In operational models, on the other hand, we typically require scenarios that represent the near future, given the current state, i.e., we need to estimate conditional distributions.