Neuronal avalanches are a local cortical phenomenon characterised by bursts of activity bracketed by periods of quiescence. It has been shown both in vivo and in vitro that these avalanches exhibit features of systems within a critical state. Locally critical system's avalanches conform to power law-like distributions. Globally these systems consist of modules exhibiting long-range temporal correlations identifiable via Detrended Fluctuation Analysis (DFA). Using an eight module oscillatory spiking neural network we analyse the correlation between these local and global criticality markers. Our findings demonstrate that locally critical modules promote long-range temporal correlations. Furthermore, when local modules are no longer critical we find that modules become uncorrelated or noisy. This suggests a strong link between local and global critical behaviour.