We study the time resolved anti-Stokes Raman spectroscopy with correlated pump and Stokes waves. When only two pump waves with relative delay are incident into a Raman medium, the Stokes waves generated by stimulated Raman scattering couple with the pump waves to generate anti-Stokes signal. Since the correlation between Stokes and the pump waves are not perfect and not quantified yet, we make a simple model fot it and calculate the normalized anti-Stokes signal intensities as a function of time delay. The broadband light regarded as chaotic field.