  The sensitivities of two periodograms are compared for weak signal planet
detection in transit surveys: the widely used Box-Least Squares (BLS) algorithm
following light curve detrending and the Transit Comb Filter (TCF) algorithm
following autoregressive ARIMA modeling. Small depth transits are injected into
light curves with different simulated noise characteristics. Two measures of
spectral peak significance are examined: the periodogram signal-to-noise ratio
(SNR) and a False Alarm Probability (FAP) based on the generalized extreme
value distribution. The relative performance of the BLS and TCF algorithms for
small planet detection is examined for a range of light curve characteristics,
including orbital period, transit duration, depth, number of transits, and type
of noise. We find that the TCF periodogram applied to ARIMA fit residuals with
the SNR detection metric is preferred when short-memory autocorrelation is
present in the detrended light curve and even when the light curve noise had
white Gaussian noise. BLS is more sensitive to small planets only under limited
circumstances with the FAP metric. BLS periodogram characteristics are inferior
when autocorrelated noise is present due to heteroscedastic noise and false
period detection. Application of these methods to TESS light curves with known
small exoplanets confirms our simulation results. The study ends with a
decision tree that advises transit survey scientists on procedures to detect
small planets most efficiently. The use of ARIMA detrending and TCF
periodograms can significantly improve the sensitivity of any transit survey
with regularly spaced cadence.
