Sequential Monte Carlo for Noncausal Processes

TL;DR

This paper introduces a Sequential Monte Carlo method for Bayesian estimation of mixed causal and noncausal models, offering faster computation, better identification, and application to financial data.

Contribution

It presents a novel SMC-based Bayesian estimation approach that improves speed, accuracy, and model identification for mixed causal/noncausal processes.

Findings

Accurate estimation and process identification demonstrated in simulations.

Method effectively determines polynomial orders and error distributions.

Application to financial data shows practical utility.

Abstract

This paper proposes a Sequential Monte Carlo approach for the Bayesian estimation of mixed causal and noncausal models. Unlike previous Bayesian estimation methods developed for these models, Sequential Monte Carlo offers extensive parallelization opportunities, significantly reducing estimation time and mitigating the risk of becoming trapped in local minima, a common issue in noncausal processes. Simulation studies demonstrate the strong ability of the algorithm to produce accurate estimates and correctly identify the process. In particular, we propose a novel identification methodology that leverages the Marginal Data Density and the Bayesian Information Criterion. Unlike previous studies, this methodology determines not only the causal and noncausal polynomial orders but also the error term distribution that best fits the data. Finally, Sequential Monte Carlo is applied to a bivariate process containing S$\&$P Europe 350 ESG Index and Brent crude oil prices.