A Case-Study of Sample-Based Bayesian Forecasting Algorithms

TL;DR

This paper compares sample-based Bayesian forecasting algorithms for real-time, nonlinear, non-Gaussian models, providing guidance on their selection and highlighting benefits and pitfalls through a financial returns case study.

Contribution

It offers a comprehensive comparison and practical guidance on sample-based Bayesian forecasting algorithms for complex time series models.

Findings

Different algorithms have distinct advantages and limitations.

Sample-based methods can be effectively applied to financial time series.

Guidelines for selecting appropriate algorithms are provided.

Abstract

For a Bayesian, real-time forecasting with the posterior predictive distribution can be challenging for a variety of time series models. First, estimating the parameters of a time series model can be difficult with sample-based approaches when the model's likelihood is intractable and/or when the data set being used is large. Second, once samples from a parameter posterior are obtained on a fixed window of data, it is not clear how they will be used to generate forecasts, nor is it clear how, and in what sense, they will be ``updated" as interest shifts to newer posteriors as new data arrive. This paper provides a comparison of the sample-based forecasting algorithms that are available for Bayesians interested in real-time forecasting with nonlinear/non-Gaussian state space models. An applied analysis of financial returns is provided using a well-established stochastic volatility model. The principal aim of this paper is to provide guidance on how to select one of these algorithms, and to describe a variety of benefits and pitfalls associated with each approach.