Sequential Monte Carlo sampling for systems with fractional Gaussian processes

In the past decades, Sequential Monte Carlo (SMC) sampling has proven to be a method of choice in many applications where the dynamics of the studied system are described by nonlinear equations and/or non-Gaussian noises. In this paper, we study the application of SMC sampling to nonlinear state-space models where the state is a fractional Gaussian process. These processes are characterized by long-memory properties (i.e., long-range dependence) and are observed in many fields including physics, hydrology and econometrics. We propose an SMC method for tracking the dynamic longmemory latent states, accompanied by a model selection procedure when the Hurst parameter is unknown. We demonstrate the performance of the proposed approach on simulated time-series with nonlinear observations.