Sequential Monte Carlo for inference of latent ARMA time-series with innovations correlated in time

Abstract

We consider the problem of sequential inference of latent time-series with innovations correlated in time and observed via nonlinear functions. We accommodate time-varying phenomena with diverse properties by means of a flexible mathematical representation of the data. We characterize statistically such time-series by a Bayesian analysis of their densities. The density that describes the transition of the state from time t to the next time instant t + 1 is used for implementation of novel sequential Monte Carlo (SMC) methods. We present a set of SMC methods for inference of latent ARMA time-series with innovations correlated in time for different assumptions in knowledge of parameters. The methods operate in a unified and consistent manner for data with diverse memory properties. We show the validity of the proposed approach by comprehensive simulations of the challenging stochastic volatility model.

Variational Bayesian inference of hidden stochastic processes with unknown parameters

“…The time series data can be modeled using a non-linear discrete time ARMA model [23]. Inspired by the problems in statistical physics, the latent states of non-linear ARMA model with unknown parameters were estimated by the importance sampling sequential Monte Carlo (IS-SMC) method and the density assisted sequential Monte Carlo (DA-SMC) method in [39]. The former method selects the joint proposal density before applying the IS to generate samples of latent states and of unknown parameters.…”

Sequential Monte Carlo bandits

“…More broadly, one can establish uniform-in-time convergence for path functionals that depend only on recent states, as the Monte Carlo error of p M (θ t−τ :t |H 1:t ) with respect to p(θ t−τ :t |H 1:t ) is uniformly bounded over time. This quick forgetting property is fundamental for the successful performance of SMC methods for inference of linear dynamical states in practice [93,94,95].…”