The intermittent emission of fluorescent light from single enzymes, quantum dots, and other nanoscale systems is often characterized by statistical correlations in the emitted signal. A one-dimensional model of such correlations in enzymes, based on a model of protein conformational fluctuations developed by Kou and Xie (Phys. Rev. Lett. 2004, 93, 180603), is formulated in the present paper in terms of the dynamics of a particle moving stochastically between "on" and "off" states under the action of fractional Gaussian noise. The model yields predictions for the short and long time behavior of the following quantities: the time correlation function, C(t), of the fluctuations of the signal intensity, the distribution, f(t), of time intervals between intensity fluctuations, and the Mandel parameter, Q(t), describing the extent of bunching or anti-bunching in the signal. At short times, C(t) and f(t) are found to decay exponentially, while, at long times, they are found to decay as power laws, the exponents being functions solely of the nature of the temporal correlations in the noise. The results are in good qualitative agreement with results from single-molecule experiments on fluorescence intermittency in the enzyme cholesterol oxidase carried out by Xie and co-workers (Science 1998, 282, 1877). The Mandel parameter, Q(t), for this model is positive at short and long times, indicating super-Poisson statistics in these limits, consistent with bunching of the fluorescent signal.