We analyze the statistics of photons originating from amplified spontaneous emission generated by a quantum dot superluminescent diode. Experimentally detectable emission properties are taken into account by parametrizing the corresponding quantum state as a multimode phase-randomized Gaussian density operator. The validity of this model is proven in two subsequent experiments using fast two-photon-absorption detection observing second-order equal-time and second-order fully time-resolved intensity correlations on femtosecond timescales. In the first experiment, we study the photon statistics when the number of contributing longitudinal modes is systematically reduced by applying well-controlled optical feedback. In a second experiment, we add coherent light from a single-mode laser diode to quantum dot superluminescent diode broadband radiation. Tuning the power ratio, we realize tailored second-order correlations ranging from Gaussian to Poissonian statistics. Both experiments are very well matched by theory, thus giving first insights into the quantum properties of radiation from quantum dot superluminescent diodes.