Fluorescence correlation spectroscopy (FCS) is a powerful tool to infer the physical process of macromolecules including local concentration, binding, and transport from fluorescence intensity measurements. Interpretation of FCS data relies critically on objective multiple hypothesis testing of competing models for complex physical processes that are typically unknown a priori. Here, we propose an objective Bayesian inference procedure for testing multiple competing models to describe FCS data based on temporal autocorrelation functions. We illustrate its performance on simulated temporal autocorrelation functions for which the physical process, noise, and sampling properties can be controlled completely. The procedure enables the systematic and objective evaluation of an arbitrary number of competing, non-nested physical models for FCS data, appropriately penalizing model complexity according to the Principle of Parsimony to prefer simpler models as the signal-to-noise ratio decreases. In addition to eliminating overfitting of FCS data, the procedure dictates when the interpretation of model parameters are not justified by the signal-to-noise ratio of the underlying sampled data. The proposed approach is completely general in its applicability to transport, binding, or other physical processes, as well as spatially resolved FCS from image correlation spectroscopy, providing an important theoretical foundation for the automated application of FCS to the analysis of biological and other complex samples.