Vibrational echo spectroscopy has become a powerful technique to study vibrational spectral diffusion in water and aqueous solutions. The dynamics of vibrational spectral diffusion is intimately related to the hydrogen bond fluctuations in liquid water and other hydrogen bonded liquids. Earlier theoretical calculations of vibrational echo spectroscopy of aqueous systems were based on classical molecular dynamics simulations involving empirical force fields of water. In the current work, we have employed the method of ab initio molecular dynamics simulation to calculate the spectral observables of vibrational echo and two-dimensional infrared (2D-IR) spectroscopy of liquid water at room temperature under Condon and cumulant approximations. The time scales extracted from the temporal decay of the frequency time correlation function (FTCF), short-time slope of three pulse photon echo (SP3E), dynamic line width (DLW), and the slope of nodal line of 2D-IR spectra are found to be in reasonably close agreement with each other which reinforces the assertion that signatures of FTCF can be captured using three pulse photon echo and 2D-IR spectroscopy.