Perils and Pitfalls of Empirical Forecasting

Abstract

It is common to use past information about the system modeled in probabilistic statistics to make predictions about the future. Especially in the area of climate modeling and forecasting this is done. Here it is argued that doing this in a purely empirical way is full of perils and pitfalls. Without knowledge of the underlying physical laws it will go wrong sooner or later. Specifically, the distribution functions are analyzed, which are normally assumed to be well-behaved gaussian-like not because there is a reason for it, but only because they don’t cause mathematical problems. Real functions (like power laws) will prohibit any statistical analysis and thus prediction model. Furthermore, correlations and extrapolations are considered. The first show that correlations come in many types and not all of them have a direct causation link. The specific case of extreme events is used as an example to highlight the difficulty and the pitfalls of empirical forecasting in general. The conclusion is that empirical forecasting cannot be used for science.