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As measured by neutron monitors the flux of galactic cosmic rays exhibits non-statistical fluctuations at all observed timescales. Many of these fluctuations can be identified with specific structures in the solar wind. There is also a rather steady diurnal variation due to cosmic ray streaming in the overall pattern of solar modulation. There is also a spectrum of fluctuations usually termed “interpl anetary scintillations” attributed to the interaction of the cosmic rays with the general magnetic turbulence in the solar wind. In recent work considering correlations between pairs of neutron monitors we found a strong correlation associated with the diurnal variation. The phase of this variation was related to the difference in asymptotic longitude of the monitors, as one might expect. However, there was a clear peak in the cross-correlations that was instead ordered by the local time difference. In the present paper we examine clear local time variations of the autocorrelations and power spectra of individual stations in an attempt to isolate the effect of the diurnal streaming anisotropy from inherent variations in the power spectrum of the fluctuations.