In this article, we investigate the interconnection and phase asynchrony between the periodicities of geomagnetic activity indices Kp, Ap, aa, and Dst according to the interplanetary magnetic field (IMF) polarities, toward (T) or away (A), during the time interval 1967–2018. For this purpose, the daily data of Kp, Ap, aa, and Dst indices during the considered period have been sorted into two groups (T and A) according to the IMF polarities. The wavelet transform (WT), the cross-wavelet transform (XWT), and the wavelet coherence (WTC) have been applied on the monthly averages of T and A groups for each geomagnetic index. Moreover, the correlation analyses (linear and running correlations) between the annual averages of T and A groups of each geomagnetic index have been investigated. The results of XWT and WTC revealed the existence of a long-term periodicity in the frequency range 8–16 yr for the monthly averages of T and A groups for aa, Kp, and Ap indices existed during the entire period. In contrast, the Dst index revealed this periodicity during the period 1980–2018. In addition, during this frequency band, both T and A groups of each geomagnetic index revealed a highly positive correlation and nearly in-phase relationship behavior. Furthermore, during the frequency band 4–8 yr, the XWT displayed a prominent periodicity that occurred for the monthly averages of T and A groups of each geomagnetic index, revealing a phase change during some time intervals. Periodicity in the range 2–4 yr for the monthly averages of T and A groups of aa, Kp,Ap, and Dst occurred in the intervals; 1967–2009 for aa and Kp, 1967–2007 for Ap, and 1976–1995 for Dst. The annual periodicity is also identified for all considered indices. Both T and A groups of Dst shared a semiannual periodicity (~187 days) during different intervals in the entire period. On the other hand, a periodicity around 0.25-yr (~90 days) appeared only near the times of solar activity maxima in the case of the T and A groups of aa, Kp, and Ap indices.
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