Statistical inference on the periodicity of irregularly sampled light curves

This thesis deals with the problem of period estimation of irregularly sampled time series, and specifically light curves of variable young stars. Knowing the period of these objects can provide important information about the stars' formation and other characteristics. The light curves are measurements of brightness over time conducted in multiple astronomical filters. We examine this problem from three different points of view. First, we need to obtain an accurate period estimate. For that purpose we introduce a weighted t-process regression model for period estimation as a flexible alternative to Gaussian process regression, since it is common for such data to exhibit a fat-tail behaviour, and we extend these models in order to include measurements from multiple astronomical filters. Secondly, we need to accompany our estimates with some credibility as to whether they represent a real periodic signal. This is usually addressed through hypothesis testing. To that end, we introduce a flexible testing scheme using saddlepoint approximation, that can be applied on a range of periodic models including Gaussian process regression. These tests are also extended for data contaminated with red noise, a type of correlated noise that usually appears in such data. Finally, we explore the asymptotic properties of simple harmonic models with additional red noise and show that this estimates are consistent and asymptotically normal. We test our results through extensive simulation studies which are reported along with an application on some real light curves from the Hunting Outbursting Young Stars citizen science project.