Search

The state-space model is a powerful statistical tool to estimate linear or non-linear discrete-time dynamic systems. This model naturally leads to the estimation problem of the time-varying parameters of the discovery-time demographic version of the susceptible-infected-recovered (SIR) model that we consider. In this paper, we consider computational methods to perform Bayesian inference on state-space models for analysing time-series data. We compare the three popular Bayesian computational methods for state-space models: the adaptive Metropolis-within-Gibbs algorithm, Liu and West's algorithm and variational approximation method based on Gaussian distributions. The performances of the three methods are compared based on synthetic datasets. Furthermore, we analyse the trend of the spread of COVID-19 in South Korea to point out the limitations of existing methods and derive meaningful results. [ABSTRACT FROM AUTHOR]

Motivated by the application to German interest rates, we propose a time‐varying autoregressive model for short‐term and long‐term prediction of time series that exhibit a temporary nonstationary 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 that of a 2‐Additive‐Factor Gaussian model as well as to the predictions of a dynamic Nelson‐Siegel model. [ABSTRACT FROM AUTHOR]