One-dimensional initial-value hybrid simulations are used to study the electromagnetic proton cyclotron anisotropy instability under the condition k¿Bo=0 where Bo is the uniform background magnetic field. The spatial correlation function of the fluctuating magnetic field is calculated at post-saturation times for aggregations of simulations corresponding to various initial values of the proton parallel &bgr; and the maximum growth rate of the instability. A statistical analysis of the results shows that the characteristic wavenumber of the correlation function may be approximately determined by linear theory; that is, by using the instantaneous values of the plasma parameters in the linear dispersion equation. In contrast the wavenumber bandwidth of the correlation function is an intrinsically nonlinear quantity and appears to depend on a weak inverse power of the fluctuating magnetic field energy density. These results predict properties of correlation functions of the enhanced proton-cyclotron-like fluctuations which may be compared against observations by the multi-spacecraft Cluster mission in the outer magnetosphere and under low flow speed conditions in the magnetosheath. ¿ American Geophysical Union 1995