A Consistent Method for Learning OOMs from Asymptotically Stationary Time Series Data Containing Missing Values
This work addresses a practical issue in time series analysis for real-world applications where data is often incomplete, though it is incremental as it builds on prior spectral learning methods.
The authors tackled the problem of learning observable operator models (OOMs) from time series data with missing values, where missingness patterns interact with the visible process, and they refined an existing algorithm to relax strong consistency conditions, achieving consistent performance in numerical experiments.
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.