  Active galactic nucleus (AGN) emission is dominated by stochastic, aperiodic
variability which overwhelms any periodic/quasi-periodic signal (QPO) if one is
present. The Auto Correlation Function (ACF) and Phase Dispersion Minimization
(PDM) techniques have been used previously to claim detections of QPOs in AGN
light curves. In this paper we perform Monte Carlo simulations to empirically
test QPO detection feasibility in the presence of red noise. Given the
community's access to large databases of monitoring light curves via large-area
monitoring programmes, our goal is to provide guidance to those searching for
QPOs via data trawls. We simulate evenly-sampled pure red noise light curves to
estimate false alarm probabilities; false positives in both tools tend to occur
towards timescales longer than (very roughly) one-third of the light curve
duration. We simulate QPOs mixed with pure red noise and determine the
true-positive detection sensitivity; in both tools, it depends strongly on the
relative strength of the QPO against the red noise and on the steepness of the
red noise PSD slope. We find that extremely large values of peak QPO power
relative to red noise (typically $\sim 10^{4-5}$) are needed for a 99.7 per
cent true-positive detection rate. Given that the true-positive detections
using the ACF or PDM are generally rare to obtain, we conclude that period
searches based on the ACF or PDM must be treated with extreme caution when the
data quality is not good. We consider the feasibility of QPO detection in the
context of highly-inclined, periodically self-lensing supermassive black hole
binaries.
