Navigating the noise: exploring black hole systems using time-series analysis

Understanding variability in accreting systems offers one of the most powerful tools for probing the innermost regions of compact objects — regions otherwise inaccessible to direct imaging. Variable signals encode information about everything from the geometry to the dynamics of the innermost flows. Time-domain astrophysics comes with immense potential, but it also brings many challenges. In this thesis, I aim to show the possibilities of time domain studies in equal measure to their caveats and pitfalls. I will demonstrate traditional techniques in the Fourier domain to brand new machine learning routines. Then I will show how no technique in this field is obsolete; they all build upon each other. This work focuses on publicly available survey data, illustrating the immense potential of what we already have and preparing us for what is to come. In a world where data is coming so fast, we might need to ask, can we keep up?