Recent literature showed that amplitude and frequency of macroeconomic fluctuations do not substantially diverge from many other extreme events, natural or human-related, once they are explained in the same time (or space) scale. Non-extensive entropy is a precious device for econometric modelling even in the case of low frequency series, since outputs evolving within the Gaussian attractor correspond to the Tsallis entropy limiting case of Tsallis q-parameter around unity. This book introduces a sub-discipline called Non- extensive Entropy Econometrics or, using a recent expression, Superstar Generalised Econometrics. It demonstrates, using national accounts-based models, that this approach facilitates solving nonlinear, complex inverse problems, previously considered intractable, such as the constant elasticity of substitution class of functions. This new proposed approach could extend the frontier of theoretical and applied econometrics.