A Bayesian Time-Varying Autoregressive Model for Improved Short- and Long-Term Prediction

TL;DR

This paper introduces a Bayesian time-varying autoregressive model tailored for predicting interest rates, effectively capturing short-term fluctuations and long-term mean reversion, with improved accuracy over existing models.

Contribution

The paper develops a novel Bayesian time-varying autoregressive model that combines short-term data-driven predictions with long-term mean reversion assumptions, enhancing interest rate forecasts.

Findings

Competitive short-term prediction accuracy.

Reasonable long-term prediction performance.

Effective regularization via Bayesian priors.

Abstract

Motivated by the application to German interest rates, we propose a timevarying autoregressive model for short and long term prediction of time series that exhibit a temporary non-stationary behavior but are assumed to mean revert in the long run. We use a Bayesian formulation to incorporate prior assumptions on the mean reverting process in the model and thereby regularize predictions in the far future. We use MCMC-based inference by deriving relevant full conditional distributions and employ a Metropolis-Hastings within Gibbs Sampler approach to sample from the posterior (predictive) distribution. In combining data-driven short term predictions with long term distribution assumptions our model is competitive to the existing methods in the short horizon while yielding reasonable predictions in the long run. We apply our model to interest rate data and contrast the forecasting performance to the one of a 2-Additive-Factor Gaussian model as well as to the predictions of a dynamic Nelson-Siegel model.