Systematic measurements of auto- and cross-correlations of photons emitted from individual $\mathrm{Cd}\mathrm{Te}∕\mathrm{Zn}\mathrm{Te}$ quantum dots under pulsed excitation were used to elucidate nonresonant excitation mechanisms in this self-assembled system. Memory effects extending over a few excitation pulses have been detected in agreement with previous reports and quantitatively described by a rate equation model, fitting a complete set of correlation and PL intensity results. The important role of single carrier trapping in the quantum dot was established. An explanation was suggested for the unusually wide antibunching dip observed previously in $X\text{\ensuremath{-}}X$ autocorrelation experiments on quantum dots under cw excitation.