  The detection of periodic signals from transiting exoplanets is often impeded
by extraneous aperiodic photometric variability, either intrinsic to the star
or arising from the measurement process. Frequently, these variations are
autocorrelated wherein later flux values are correlated with previous ones. In
this work, we present the methodology of the Autoregessive Planet Search (ARPS)
project which uses Autoregressive Integrated Moving Average (ARIMA) and related
statistical models that treat a wide variety of stochastic processes, as well
as nonstationarity, to improve detection of new planetary transits. Providing a
time series is evenly spaced or can be placed on an evenly spaced grid with
missing values, these low-dimensional parametric models can prove very
effective. We introduce a planet-search algorithm to detect periodic transits
in the residuals after the application of ARIMA models. Our matched-filter
algorithm, the Transit Comb Filter (TCF), is closely related to the traditional
Box-fitting Least Squares and provides an analogous periodogram. Finally, if a
previously identified or simulated sample of planets is available, selected
scalar features from different stages of the analysis -- the original light
curves, ARIMA fits, TCF periodograms, and folded light curves -- can be
collectively used with a multivariate classifier to identify promising
candidates while efficiently rejecting false alarms. We use Random Forests for
this task, in conjunction with Receiver Operating Characteristic (ROC) curves,
to define discovery criteria for new, high fidelity planetary candidates. The
ARPS methodology can be applied to both evenly spaced satellite light curves
and densely cadenced ground-based photometric surveys.
