Merging VAR and factor model with One-sided Dynamic Autoregressive Principal Components

Abstract

This paper proposes a multivariate model structure to forecast high-dimensional time series. The model extracts components as linear combinations of the time series present and past values. The components follow autoregressive processes and are called One-sided Dynamic Autoregressive Principal Components. They contain signals useful for forecasting that are shared across time series. The original time series are then reconstructed from the fitted component values. This model contains three stages of transmission of information: from the time series to the components, from the components to the components’ future, and from the components back to the original time series. The effects of these stages are captured by different sets of parameters, which are estimated by minimising reconstruction error. Special cases of this general specification cover a range of models including constrained Vector Autoregression and factor models. Forecasting performance is examined using simulation and empirical applications.