We report statistically measurable responses of the Northern Annular Mode (NAM) and the equatorial stratospheric Quasi-biennial Oscillation (QBO) to solar wind dynamic pressure. When December to January solar wind dynamic pressure is high, the Northern Hemispheric (NH) circulation response is marked by a stronger polar vortex and weaker sub-tropical jet in the upper to middle stratosphere. As the winter progresses, the Arctic becomes colder and the jet anomalies shift poleward and downward. In spring, the polar stratosphere becomes anomalously warmer. At solar maxima, significant positive correlations are found between December to January solar wind dynamic pressure and the mid- to late winter NAM all the way from the surface to 20 hPa, implying a strengthened polar vortex, reduced Brewer-Dobson circulation and enhanced stratosphere-troposphere coupling. The combined effect of high solar UV irradiance and high solar wind dynamic pressure in the NH mid- to late winter is enhanced westerlies in the extratropics and weaker westerlies in the subtropics, indicating that more planetary waves are refracted towards the equator. At solar minima, there is no correlation in the NH winter but negative correlations between December to January solar wind dynamic pressure and the NAM are found only in the stratosphere during spring. Statistical evidence of a possible modulation of the equatorial stratospheric Quasi-biennial Oscillation (QBO) by the solar wind dynamic pressure is also provided. When solar wind dynamic pressure is high, the QBO at 30-70 hPa is found to be preferably more easterly during July to October. These lower stratospheric easterly anomalies are primarily linked to the high frequency component of solar wind dynamic pressure with periods shorter than 3-years. In annually and seasonally aggregated daily averages, the signature of solar wind dynamic pressure in the equatorial zonal wind is characterized by a vertical three-cell anomaly pattern with westerly anomalies both in the troposphere and the upper stratosphere and easterly anomalies in the lower stratosphere. This anomalous behavior in tropical winds is accompanied by a downward propagation of positive temperature anomalies from the upper stratosphere to the lower stratosphere over a period of a year. These results suggest that the solar wind dynamic pressure exerts a seasonal change of the tropical upwelling which results in a systemic modulation of the annual cycle in the lower stratospheric temperature, which in turn affects the QBO during Austral late winter and spring. These results suggest possible multiple solar inputs. Their combined effect in the stratosphere may cause refraction/redistribution of upward wave propagation and result in projecting the solar wind signals onto the NAM and the QBO. The route by which the effects of solar wind forcing might propagate to the lower atmosphere is yet to be understood.