An algorithm for non-parametric estimation in state-space models

TL;DR

This paper introduces a novel non-parametric estimation algorithm for state-space models by combining SEM and SMC techniques, enhancing flexibility in modeling complex time series data.

Contribution

It proposes a new algorithm that integrates SEM and SMC methods for non-parametric inference in state-space models, addressing limitations of parametric approaches.

Findings

Effective in toy model simulations

Demonstrates applicability to environmental data

Improves flexibility over parametric models

Abstract

State-space models are ubiquitous in the statistical literature since they provide a flexible and interpretable framework for analyzing many time series. In most practical applications, the state-space model is specified through a parametric model. However, the specification of such a parametric model may require an important modeling effort or may lead to models which are not flexible enough to reproduce all the complexity of the phenomenon of interest. In such situations, an appealing alternative consists in inferring the state-space model directly from the data using a non-parametric framework. The recent developments of powerful simulation techniques have permitted to improve the statistical inference for parametric state-space models. It is proposed to combine two of these techniques, namely the Stochastic Expectation-Maximization (SEM) algorithm and Sequential Monte Carlo (SMC) approaches, for non-parametric estimation in state-space models. The performance of the proposed algorithm is assessed through simulations on toy models and an application to environmental data is discussed.