This research explores how magnetic field and plasma density in the solar wind are auto-correlated across timescales from minutes to years, characterized by correlation functions. The correlation function has a one-to-one correspondence with the power spectrum, which describes how energy is distributed across timescales. A well-known feature in the solar wind low-frequency spectrum is the $1/f$ noise, conventionally found at frequencies smaller than the inertial range of turbulence and truncated by the point spectral features associated with solar rotation. We examine how the correlations and spectra vary by wind speed and solar cycle phases, and show for the first time that this $1/f$ behavior underlies the band of spectral peaks associated with solar rotation.