Scalable Functions Used for Empirical Forecasting

Empirical forecasting is the science of using past data to predict the future, without physical modeling. For these, probability functions are used, normally bell-shaped Gaussian or Gaussian- like. Taleb in his book the Black Swan introduces for this purpose the concept of scalable functions. Here it is shown that the only scalable functions are power-law functions and they can be treated as one and the same. Moreover, the analytical problems of these functions are discussed. Scalable functions are inadequate for empirical forecasting.