Statistics and correlations of single-molecule sequences of modulated reactions are explicitly evaluated in the stochastic rate representation. The memory function, introduced through the Gaussian approximation of the stochastic rate expression, characterizes the correlation in single-molecule rate processes in a formalism similar to the stochastic line shape theory. Within this formalism, the on-time correlation is shown to approximate the memory function of the fluctuating rate at discretized effective time separations. A new measurement, the two-event number density, is proposed as a means to map out the memory function over the complete time range. Confirmed by numerical calculations, these relations quantify dynamic disorder caused by conformational fluctuations and hence are useful for analyzing single-molecule kinetics.