Bayesian Modeling and Forecasting of High Dimensional Long Range Dependent Time Series

Abstract

The increasing availability of large-scale time series data presents significant challenges for forecasting. While long-range dependence (LRD) enables long-term forecasting, the sample size is often too small relative to the number of parameters. This talk addresses this issue through two key themes: Bayesian vector heterogeneous autoregressive (BVHAR) models with the Minnesota prior and adaptive hierarchical priors. The BVHAR framework incorporates the Minnesota prior, a well-regarded approach in economic time series analysis. BVHAR with an independent Normal-Wishart prior achieves posterior consistency and demonstrates strong forecasting power on financial datasets. Additionally, various shrinkage priors are integrated into the VHAR model, along with a sparsification method. Notably, this work shows that the Generalized Double Pareto (GDP) shrinkage prior can be a promising candidate for time series modeling. The BVHAR model, particularly when implemented with the GDP prior, exhibits excellent long-term forecasting performance for macroeconomic time series.