  Periodograms are widely employed for identifying periodicity in time series
data, yet they often struggle to accurately quantify the statistical
significance of detected periodic signals when the data complexity precludes
reliable simulations. We develop a data-driven approach to address this
challenge by introducing a null-signal template (NST). The NST is created by
carefully randomizing the period of each cycle in the periodogram template,
rendering it non-periodic. It has the same frequentist properties as a periodic
signal template regardless of the noise probability distribution, and we show
with simulations that the distribution of false positives is the same as with
the original periodic template, regardless of the underlying data. Thus,
performing a periodicity search with the NST acts as an effective simulation of
the null (no-signal) hypothesis, without having to simulate the noise
properties of the data. We apply the NST method to the supermassive black hole
binaries (SMBHB) search in the Palomar Transient Factory (PTF), where Charisi
et al. had previously proposed 33 high signal to (white) noise candidates
utilizing simulations to quantify their significance. Our approach reveals that
these simulations do not capture the complexity of the real data. There are no
statistically significant periodic signal detections above the non-periodic
background. To improve the search sensitivity we introduce a Gaussian
quadrature based algorithm for the Bayes Factor with correlated noise as a test
statistic, in contrast to the standard signal to white noise. We show with
simulations that this improves sensitivity to true signals by more than an
order of magnitude. However, using the Bayes Factor approach also results in no
statistically significant detections in the PTF data.
