Decoupling of local and global behaviour for the Dagum Random Field and related models E. Porcu 1 , O. Nicolis 2 and J. Mateu 1 1 Departamento de Matem´ aticas, Universitat Jaume I, Castell´ on, Spain 2 Departimento di Ingegneria, Universit` a degli studi di Bergamo, Italy Abstract: We present a class of isotropic correlation functions that decouples the local and global behaviour of its associated random field. An intensive simulation study shows the feature of this new class in comparison with another well-known class of correlation functions possessing the decoupling feature. Keywords: Correlation function; Fractal dimension; Hurst effect; Isotropy 1 Introduction The knowledge of the local and global properties of a weakly stationary random field finds an intimate connection with that of its associated corre- lation function. The words local and global find a traditional formalism in the theory of, respectively, fractal or Haussdorf dimension and Hurst effect. Roughly speaking, the former is a roughness measure of a profile or surface of R n , while the latter reflects possible long memory dependence in a time series or a random field. The term self-similar or self-affine, coined in Mandelbrodt Essay (1982) means that local properties of a time series or random field are somehow reflected in the global ones and vice versa. The assumption of self-similarity is reasonable for many natural phenom- ena; at the same time, owing to an evident lack of methodological alter- natives, only very few scientists have constructively criticised a somehow mechanical use of this assumption. Quite recently, the cautious criticism of Constantine and Hall (1994) has induced the natural counterbalance of self-affinity, the so-called decoupling. The epistemic behind this word relates to the possibility of an independent treatment of the fractal and long memory parameters. This is in clear antithesis with the assumption of self-similarity, and, if verifiable, can be very useful as local and global parameters may be estimated separately. At the same time, no rigorous methodology is available. Thus, any inspection for potential decoupling needs caution, as reasonable conclusions can be reached through ad hoc methods, such as intensive simulation studies and descriptive graphical tools.