A Consistent Method for Learning OOMs from Asymptotically Stationary Time Series Data Containing Missing Values

In the traditional framework of spectral learning of stochastic time series models, model parameters are estimated based on trajectories of fully recorded observations. However, real-world time series data often contain missing values, and worse, the distributions of missingness events over time are often not independent of the visible process. Recently, a spectral OOM learning algorithm for time series with missing data was introduced and proved to be consistent, albeit under quite strong conditions. Here we refine the algorithm and prove that the original strong conditions can be very much relaxed. We validate our theoretical findings by numerical experiments, showing that the algorithm can consistently handle missingness patterns whose dynamic interacts with the visible process.