Inelastic neutron scattering measurements of paramagnetic SrCo$_{2}$As$_{2}$ at T=5 K reveal antiferromagnetic (AFM) spin fluctuations that are peaked at a wavevector of $\textbf{Q}_{\mathrm{AFM}}=(1/2,1/2,1)$ and possess a large energy scale. These stripe spin fluctuations are similar to those found in $A$Fe$_{2}$As$_{2}$ compounds, where spin-density wave AFM is driven by Fermi surface nesting between electron and hole pockets separated by $\textbf{Q}_{\mathrm{AFM}}$. SrCo$_{2}$As$_{2}$ has a more complex Fermi surface and band structure calculations indicate a potential instability towards either a ferromagnetic or stripe AFM ground state. The results suggest that stripe AFM magnetism is a general feature of both iron and cobalt-based arsenides and the search for spin fluctuation-induced unconventional superconductivity should be expanded to include cobalt-based compounds. ; Comment: This is a companion paper to arXiv:1306.5222 with journal reference Phys. Rev. B 88, 014526 (2013)