  One of the main features of interest in analysing the light curves of stars
is the underlying periodic behaviour. The corresponding observations are a
complex type of time series with unequally spaced time points and are sometimes
accompanied by varying measures of accuracy.
  The main tools for analysing these type of data rely on the periodogram-like
functions, constructed with a desired feature so that the peaks indicate the
presence of a potential period. In this paper, we explore a particular
periodogram for the irregularly observed time series data, similar to Thieler
et. al. (2013). We identify the potential periods at the appropriate peaks and
more importantly with a quantifiable uncertainty. Our approach is shown to
easily generalise to non-parametric methods including a weighted Gaussian
process regression periodogram. We also extend this approach to correlated
background noise. The proposed method for period detection relies on a test
based on quadratic forms with normally distributed components. We implement the
saddlepoint approximation, as a faster and more accurate alternative to the
simulation-based methods that are currently used. The power analysis of the
testing methodology is reported together with applications using light curves
from the Hunting Outbursting Young Stars citizen science project.
