A Bayesian framework for functional time series analysis

TL;DR

This paper presents a flexible Bayesian framework for analyzing functional time series, extending dynamic linear models to Banach spaces, with practical implementation via MCMC methods.

Contribution

It introduces a novel Bayesian approach for functional time series analysis using Banach-space models, enhancing flexibility and ease of implementation.

Findings

Framework applicable to continuous functions and other data types.

Uses stochastic process theory for prior and transition specification.

Employs standard MCMC methods for posterior inference.

Abstract

The paper introduces a general framework for statistical analysis of functional time series from a Bayesian perspective. The proposed approach, based on an extension of the popular dynamic linear model to Banach-space valued observations and states, is very flexible but also easy to implement in many cases. For many kinds of data, such as continuous functions, we show how the general theory of stochastic processes provides a convenient tool to specify priors and transition probabilities of the model. Finally, we show how standard Markov chain Monte Carlo methods for posterior simulation can be employed under consistent discretizations of the data.