Researchers have studied the interplanetary magnetic field (IMF) and solar-wind (SW) parameters that influence the development of geomagnetic storms for more than a decade. This study utilised newly developed tools for investigating the association between solar and interplanetary plasma parameters along with geomagnetic (GM) indices during two different geomagnetic storms of varying intensity that occurred on 20 November 2003 (SYM-H = -490 nT) and 22 June 2015 (SYM-H = -139 nT). As the largest storm in Solar Cycle (SC)-23 and the second largest in SC-24, these events were deliberately chosen to represent extreme space weather activity. The study of these severe geomagnetic events provides a unique opportunity to better understand the coupling nature between the solar wind-magnetosphere-ionosphere system. Cross wavelet analysis (XWT) exposes high common power regions between the solar wind velocity (Vsw) and interplanetary magnetic field component (IMF-Bz), plasma pressure (Psw), plasma density (Nsw), Geomagnetic Auroral Electrojet (AE) index and Symmetrical Ring Current Index (SYM‐H). Another useful tool is wavelet transform coherence (WTC), which we have applied to measure how coherent the XWT is in time-frequency space. Thus, the local correlation between two continuous wavelet transforms (CWTs) can be conceived of as WTC. Moreover, we examined the relationship among the solar wind parameters during storm events using detrended cross-correlation analysis (DXA) with possible explanations. The study’s findings will demonstrate that the suggested methods are a simple, effective, and robust method for gaining deeper insight into the complex spatiotemporal characteristics of time series.