"Sequential Monte Carlo with Parameter Learning For Non-Markovian Processes"

Abstract: We consider a state-space model in which the unobserved process exhibits either long-range dependence or antipersistence. Our goal is to estimate both the unobserved state and the unknown parameters. For this, we propose a sequential Monte Carlo method for a combined parameter and state estimation based on smoothing of the sample points of model parameters. We also prove a Central Limit Theorem for the state and parameter filter. We illustrate our results with a simulation study and we apply our approach to S&P 500 data in the context of a fractional stochastic volatility model.

Host: Jose Figueroa-Lopez