The basic theoretical results of GMDH consists of:

1. It was proved that shortened non-physical forecasting models is better than contentative physical model on error criterion.
   (See: Aksenova,T.I. and Yurachkovsky,Yu.P. A Characterization at Unbiased Structure and Conditions of Their J-Optimality, Sov. J. of Automation and Information Sciences, vol.21, 4, 1988, pp.36-42)
2. It was proved the convergence of multilayered GMDH algorithms.
   (See: Ivakhnenko,A.G. and Yurachkovsky,Yu.P., Modelirovanie Slozhnykh System po Exsperimentalnym Dannym (Modeling of Complex Systems after Experimental Data). Moscow: Radio i svyaz, 1986, 118p.)