Modelling Under Risk and Uncertainty: An Introduction to Statistical, Phenomenological and Computational Methods

1.5 Forecast and Time-Based Modelling in Weather, Operations Research, Economics or Finance

An essential area of application of modelling under uncertainty with considerable practical value and on-going research involves the prediction of variables of interest under uncertainty over future times of interest. Think of meteorological forecast, operations research and stochastic optimisation be it in econometrics (micro-economic market forecast or macro-economic growth forecast), energy or asset management, financial market forecast and portfolio analysis and so on (see, e.g. the survey of Tay and Wallis, 2000 or Elliott, Granger, and Timmermann, 2006).

This area shares essential common features with the framework developed above (in particular IPRA or UASA). Again, the decision-maker is interested in the prediction of given variables of interest characterising an underlying system, process, portfolio or market, which is itself impacted by a number of uncertain events, behaviours or mechanisms, in order to typically select the best actions to take (the controllable variables) such as operational actions best suited to the likely weather or market demand or portfolio allocations. A quantity of interest or risk measure is set to optimise performance or control the risk budget. For instance, the power supply-demand balance would be controlled over a future time period through a prescribed maximal frequency of events with negative balance. Otherwise, the value of asset portfolios over ...