The starting point is the discussion of the interconnections between such notions as adaptive methods,selector statistics,model choice,model verification,parameter identification and parameter estimation.Next, the characterization of time series models introducing a modelled process ξ by means of an auxiliary process η is given in terms of derived and primitive models, and this is used to present some typical schemes of evolution of statistics,namely that of solving difficult problems by means of easy standard ones.It is shown how parameter identification is being used in the context.Finally, some characteristic approaches to parameter identification are mentioned,including methods based on residuals, Akaike's information criterion,Box-Jenkins diagnostic checking and Couts-Crether-Nerlove graphical methods.