This work examines the properties and mathematical structure of factorized time correlation (FTC) diagram analysis in a general context. The goal is to extract general principles and analytic behavior that are not tied to any particular phenomenon in physics. It is hoped that this will provide a basis for expanded use of FTC diagram analysis beyond its current employment in the study of noisy light-based nonlinear optical spectroscopy. Furthermore, the concept of indirect correlation in a two-channel system driven by twin stationary circular Gaussian stochastic inputs is defined and discussed both analytically and through FTC diagram analysis.