To understand the phenomenon of frequent reversals of axial geocentric dipole fields it is essential to understand the spectral structure of geomagnetic reversal series and search for possible exogenetic (cosmic) factors associated with its dynamic behaviour. A scheme of Walsh spectrum analysis (which is more efficient and appropriate for binary processes as compared to Fourier Spectrum Analysis and Maximum Entropy Method), has been applied, for the first time, to the available world-wide paleomagnetic measurements during phanerozoic (last 570 million years). The results postulate long-term cyclicity in magnetic stratigraphy with reversal periods of 285, 114, 64, 47 and 34 million years with distinct resolution. The similar analysis was further repeated by dividing the total record in two sub-series. These results indicate mean periods of 71, 47 and 32- m.y. These peaks are statistically significant at 90% confidence level. These results, thus, question the widely accepted theory of randomness of geomagnetic reversal for long-period sequence. Surprisingly, the maximum spectral power is found for the Cosmic year (285 m.y.) Term (period of complete revolution of solar system around the Milky way galactic centre). The other reversal periods correspond nicely with the solar system's periods of galactocentric radial motion, interaction of spiral density wave with galactic orbit and solar oscillation in and outside of orbital plane. Such a remarkable correlation and harmony between observed gravitational phenomena and terrestrial records of electromagnetic processes on the cosmic scale appear to be of fundamental importance in macroscopic physics.