Filtering of nonlinear time-series coupled by fractional Gaussian processes

In this paper we consider a set of time-series that are coupled by latent fractional Gaussian processes. Specifically, we address time-series that combine idiosyncratic short-term and shared long-term features. The long-memory is modeled by fractional Gaussian processes, whereas the short-memory properties are captured by linear models of past data. The observations are nonlinear functions of the latent states and therefore, for inference of the latent states we resort to a sequential Monte Carlo sampling technique. The proposed solution is evaluated via simulations of an illustrative practical scenario.