The Time-Varying Multivariate Autoregressive Index Model

Many economic variables are characterized by changes in their conditional mean and volatility, and time-varying Vector Autoregressive Models are often used to handle such complexity. Unfortunately, as the number of series grows, they present increasing estimation and interpretation issues. This paper tries to address this problem by proposing a Multivariate Autoregressive Index model that features time-varying mean and volatility. Technically, we develop a new estimation methodology that mixes switching algorithms with the forgetting factors strategy of Koop and Korobilis (2012). This substantially reduces the computational burden and allows one to select or weigh the number of common components, and other data features, in real-time without additional computational costs. Using US macroeconomic data, we provide a forecast exercise that shows the feasibility and usefulness of this model.