The average characteristics of the diurnal and semi-diurnal anisotropy of cosmic ray intensity at relativistic energies have been obtained by using data from the worldwide grid of neutron monitor for the period 1989 to 1996. The complex behaviour of the diurnal amplitudes and time of maxima (phase) and its association with the Ap index on a long-term and day-to-day basis have been studied. Even though the general characteristics, on a yearly average basis, have not changed significantly during this period, both the diurnal and semi-diurnal amplitudes and phases vary significantly, besides significant changes being observed for different interplanetary conditions on a short-term basis. It is found that the relationship between the Ap index and the diurnal vector is out of phase during the period 1991 to 1995. On a long-term basis, the correlation of diurnal variation with Ap index has been found to vary during the solar cycle. On a short-term basis, it has been observed that the high Ap days are usually associated with higher amplitudes with phase shifted to earlier hours.

We applied fast Fourier transform techniques and Morlet wavelet transform on the time series data of coronal index, solar flare index, and galactic cosmic ray, for the period 1986–2008, in order to investigate the long- and mid-term periodicities including the Rieger ($\sim$130 to $\sim$190 days), quasi-period ($\sim$200 to $\sim$374 days), and quasi-biennial periodicities ($\sim$1.20 to $\sim$3.27 years) during the combined solar cycles 22–23. We emphasize the fact that a lesser number of periodicities are found in the range of low frequencies, while the higher frequencies show a greater number of periodicities. The rotation rates at the base of convection zone have periods for coronal index of $\sim$1.43 years and for solar flare index of $\sim$1.41 year, and galactic cosmic ray, $\sim$1.35 year, during combined solar cycles 22–23. In relation to these two solar parameters (coronal index and solar flare index), for the solar cycles 22–23, we found that galactic cosmic ray modulation at mid cut-offrigidity (${\rm Rc} = 2.43$GV) is anti-correlated with time-lag of few months.